FR2524813A1 - Spatial puzzle based on polyhedron - having central part with tubular axles on which pieces pivot and other pieces slide - Google Patents

Abstract

The spatial puzzle is based on a regular or an irregular polyhedron. It has a central part with equi-angular tubular axis that point towards the faces of the outer solid. Each axis carries a piece (2) that pivots on the axle. Intermediate pieces (4) have curved extensions that fit together with the edges of the pivoting pieces. The summit pieces (3) form the corners (S1,S2,S3,S4) of the solid and have projections on two faces that can slide in grooves in the intermediate pieces. Parts of the solid can be turned around the axle passing through the centre of each part.

Description

SPATIAL LOGICAL GAME.

 The present invention relates to a spatial logic game of the type in which a number of solid elements, arranged in any relative configuration, must be brought by the player, in a given configuration.

 We already know a spatial logic game of this type, which can have the outside, the shape of a cube, a sphere or another body, and which consists of a central piece from which six aligned axes start. two by two along the three axes of an orthonormal coordinate system and twenty-six other parts, six of which are of a kind, twelve of a second kind and eight of a third kind, are assembled together and with said axes that one can rotate around an axis, in both directions, the nine parts forming a face of the body. The latter, which may have any external shape, has been realized, in practice, in the form of a cube, each face of which is divided into nine parts, the six faces of the cube having, for example, The goal of the game is, from any configuration, to bring the different pieces back into the configuration in which each face of the cube is single-colored.

 This known device, of great ingenuity, has, however, some disadvantages. First, the difficulty presented by the game is not enough for all players, especially as the structure of this game is based on an orthonormal frame, which corresponds to the ordinary visual and mental representation of space . However, for some players, this game is still too complex and is not used, players are quickly discouraged.

 In addition, this game, in its configuration in which it has nine exposed parts per face, necessarily has a fixed part relative to the axis, namely the center piece of the face, which facilitates the tracking for the player.

 The present invention proposes to remedy these drawbacks and to provide spatial logic games of particular interest to the player.

 The invention therefore relates to the novel spatial logic game characterized in that it is constituted on the basis of a regular polyhedron selected from the group formed by the tetrahedron, octahedron, dodecahedron and icosahedron, and a non-regular polyhedron such as the "pointed cube" or the "pointed dodecahedron", said set comprising, a central piece having, for the tetrahedron and octahedron, four equiangular axes extending in the four directions of space, for the dodecahedron and icosahedron, twelve equiangular axes extending in the twelve directions of space, for the pointed cube, fourteen axes and for the dodecapoint thirty-two axes, each axis carrying a pivoting piece pivotally mounted about said axis and adjacent rooms, hereinafter called intermediate rooms, six in the case of the tetrahedron and octahedron, thirty in the case of the dodecahedron and the icosahedron, twelve of a kind and twenty-four of another kind in the case of the pointed cube, thirty of one kind and sixty of another kind in the case of the dodecapointu, said intermediate pieces being able, if necessary, to present themselves facets extending substantially on the same geometrical sphere, said intermediate parts themselves then forming intermediate parts for retaining corresponding spans of adjacent parts, hereinafter referred to as vertex parts, the non-visible facets, mutually in contact, of parts intended to move relative to each other being shaped to substantially allow mutual sliding of said parts, radial retaining means being provided to prevent radial spacing between each piece and the central piece.

 The contact facets of said parts are either spherical, to ensure the radial retention of the parts, either planar or conical, to ensure their pivoting plan on plane or cane on cane, said planes being orthogonal to the corresponding axes of rotation, and said cones being of revolution around the aforementioned axes of rotation. However, in the case of the tetrahedron, octahedron and dodecahedron in particular, and even possibly for the other solids, it may be advantageous to substitute curved (spherical or conical) surfaces for flat (or planar) surfaces. pieces) inscribed or circumscribed in said curves, insofar as this substitution does not create between the pieces a game such that it harms the cohesion of the assembly during the pivoting.

 From the point of view of the external appearance, the logic games according to the invention can have the shape not only of the actual polyhedra having a fixed number of identical faces, but also of solids, which can be obtained by prolonging or modifying in some way the apparent faces of the polyhedron, while respecting the aforementioned planes or sliding cones.

 Thus the games are constituted "on the basis" of a polyhedron as claimed, it being understood that the forms of the apparent faces and facets which will be described is reported for the convenience of the expression in the case of the game having actually the appearance of the polyhedron considered.

 The pivoting parts, as we have seen, cooperate with the axes of the central piece, each pivot piece being rotatable about a given axis. In fact, the pivoting part can physically have an axis oriented towards the central piece and being housed in a bearing presented by it. However, it is preferred that it is the center piece which presents the physical axes themselves so as to move the pivoting zone away from the geometric center of the logic game. Thus, the pivoting piece may comprise a short section of axis coming in the extension of the corresponding axis of the central part, the pivotal mounting being effected by making, for example, penetrate the axis of the pivot piece in an orifice presented by the axis of the central part.La pivoting part may also be devoid of any physical axis and present itself a pivotally receiving bearing, the end of an axis carried by the central part.

The connection between the central part and the pivoting part, intended to allow pivoting of the pivoting part about the axis but to prohibit a radial distance from the pivoting part relative to the central part, is made by snapping. However, any other form of connection may be provided.

 Preferably, the mounting of the pivoting parts on the axes can be effected by allowing a certain elastic axial displacement so as to reduce the resistance to pivoting resulting from the friction between the facets in contact. Furthermore, a radial detent system comprising three, four or five notches depending on whether the parts are called to rotate one third, quarter or fifth turn, takes advantage of this elasticity by giving each of three, four or five positions that must occupy the pivoting piece after the pi pi pivoting, a character of stability necessary for the proper functioning of the system.

 The intermediate pieces may comprise extensions which are disposed in a substantially spherical facet of the pvorPent piece so as to be radially retained by the latter while being able to move relative to the central part, by sliding the facets mutually. In fact, the spherical facet of the pivoting part which serves to retain said extensions of the intermediate parts may, in certain cases, not be perfectly spherical and the corresponding spans of the extensions of the intermediate parts may also not be spherical but planar in planes substantially tangent to the geometric sphere at the considered location. It is the same for the crown pieces which, for their part, are held radially by the intermediate pieces. In another embodiment of the invention, the radial retaining means constituted by the substantially spherical shaped facets in cooperation with the corresponding extensions of the parts adjacent to those carrying the facets may be omitted and replaced for all or part of the parts. by fine radial extensions of each piece, each radial extension having an end each penetrating into a groove carried by a spherical central piece, the grooves being circular and corresponding homothetically to the movements to be followed by the corresponding piece. Preferably, the end of this arm may be slightly bulged so as to allow depression by deformation in the groove, opposing subsequent extraction graceful snapping thus achieved.

 The different pieces are preferably molded in one piece. However, for ease of assembly, it is possible to provide certain parts in the form of several subassemblies, preferably only two subassemblies, which are assembled. Thus, in the case of the icosahedron, the pointed cube and the dodecapointu, it is preferred that the vertex piece, that is to say the piece that contributes to forming an external face of the icosahedron, of the cube pointed and dodecapointed, consists of two parS, namely an inner part and an outer part, the outer part, ---------------------- being mounted in last place on the internal part already assembled, preferably snap-fastening.

Other advantages and features of the invention will become apparent on reading the following description, given by way of non-limiting example, and with reference to the appended drawing in which
FIG. 1 represents a perspective view of a tetrahedral clearance according to the invention with the schematic separation according to a sliding plane;
FIG. 2 represents a perspective view of a central part of the tetrahedral game.
FIG. 3 represents a perspective view of a pivoting part of this game
FIGS. 4, 5 and 6 represent respectively a bottom view, a side view and a perspective view of an intermediate piece of this game
FIG. 7 represents a perspective view of a top piece of this game;
- Figure 8 shows a perspective view of an octahedral game according to the invention with schematic separation according to a sliding plane;
FIGS. 9 and 10 show respectively a bottom view and a side view of a top piece of this game
FIG. 11 represents a perspective view of a top piece of this game, actually occupying the center of a face of the octahedron;
FIG. 12 represents a perspective view of a dodecahedron clearance according to the invention; --------------
FIG. 13 represents an exploded perspective view of the parts of a face of this dodecahedral game;
FIG. 14 represents a perspective view of a central piece of this game
FIG. 15 represents a perspective view of a pivoting part of this game
FIGS. 16, 17 and 18 show respectively a perspective view, an axial sectional view with partial tearing and a cross-sectional view of an intermediate piece of this game
Figures 19, 20 and 21 show respectively a perspective view, a bottom view and an elevational view of a top piece of this game;
FIG. 22 represents a perspective view of an icossedric game with schematic separation according to a sliding plane.
FIG. 23 represents a schematic perspective view of a central part of this game, with a pivoting piece
FIG. 24 represents a schematic perspective view of an intermediate piece of this game
FIG. 25 represents a schematic perspective view of a summit piece of this game
FIG. 26 represents a schematic perspective view of the assembly of several of the pieces of this set;
FIG. 27 represents a perspective view of a pointed cube
FIG. 28 represents the cleavage planes of this pointed cube
FIG. 29 represents an exploded partial view of this pointed cube
FIGS. 30 and 31 represent perspective views of the two types of intermediate pieces of this pointed cube
FIG. 32 represents a view of a vertex piece of this pointed cube;
FIG. 33 represents a color scheme of this pointed cube
FIG. 34 represents a perspective view of a pointed dodecah
FIG. 35 represents the cleavage planes of this pointed dodeca.
- Figure 36 shows in perspective -sa central part
FIG. 37 represents a view of the crown pieces of this pointed dodecah
- Figure 38 shows the scheme of co1oratn this dodéca-pointed with front and rear views.

 The figures also include reference numerals, indications of angular dimension (in degrees) or metric (in millimeters), represented space games. These obey the mathematical imperatives of the considered solids, but technical considerations may suggest other dimensions (metrics) also responding to the same mathematical imperatives. We will refer to these figures to read the dimensions of the parts considered.

 Reference is first made to FIGS. 1 to 6.

Referring to FIG. 1, there is a game having the external shape of a tetrahedron, whose four faces have been referenced A1, A2, A3 and A4 (only
Al and A2 being visible) as well as the opposite peaks
S1, S2, S3 and S4. In FIG. 1, the tetrahedron has been represented with schematic separation along a sliding plane parallel to the face A2, that is to say perpendicular to the axis passing through S9, the center of the tetrahedron 01 and the center of the A2 face; in fact, the tetrahedron is collected in the normal state.

 The tetrahedron is composed of fifteen three-dimensional pieces of four different types, namely a central piece 1, four pivoting pieces 2, four crown pieces 3 and six intermediate pieces 4. It can be seen in FIG. A4 of the tetrahedron is divided into seven surfaces corresponding to the facets visible in this plane of a pivot piece 2, three sonnet pieces 3 and three lateral pieces.

 Referring to Figure-2, we see the central part 1. This has the form of a tetrapod with four branches from the same geometric center 01 and centered on the geometric axes connecting the center 01 of the tetrahedron to respective centers of the faces Al to A4.

Each branch of the quadrupole has a central opening nini a shallow lip lip followed by a cylindrical wall whose diameter is slightly greater than the diameter of the lip 1b.

 Referring to Figure 3, there is shown a pivoting part of the tetrahedron 2. This piece has an upper plate, whose equilateral triangular facet 2a is visible on the corresponding face of the tetrahedron. The three lateral facets of the plate 2b are arranged in the respective planes formed by the faces of a triangular geometric pyramid having as a vertex 01, said faces being truncated by a geometric sphere of center 01. Consequently, the lower non-visible facet 2 of the plate has the shape of a triangular spherical sector centered on 01. In the center of this spherical sector 2Q, and in a radial direction towards the center 01, extends an arm 2c having the same diameter as the arms la, and the radial notch fits into that of the piece la. At the end of the arm 2c is mounted a coaxial head 2d and which, preferably, is capable of a small axial movement relative to the arm 2c, for example by being guided therein and biased towards the arm 2c by a internal spring (not shown). The head 2d has, for example, towards its free end, a frustoconical chamfer facilitating introduction into the lip 1b, then a part 2e, whose diameter is slightly greater than that of the lip, followed by a part 2f forming a kind of collar.

 It is thus understood that it is thus possible to introduce the head 2d into the hole of one of the arm of the quadrupole 1, the lipbone pocketing the extraction, a unless applying a significant force. As a result, the part 2 once mounted in the corresponding arm of the tetrapod 1, it will be possible to rotate the plate around the geometric axis of the corresponding arm, the notching opposing a reduced resistance to rotation but allowing the piece to preferentially adopt one of the three angular positions that it possesses when the game has its normal external tetrahedral shape.

 Referring to FIGS. 4 to 6, an intermediate part 4 is seen. This part has two visible external facets 4a forming a dihedral with the edge of the tetrahedron, each face 4a having the shape of a trapezoid with angles of 60 and 60 respectively. 1200, the small base of the trapezium having the same length as the caté of the triangular facet 2a of a pivoting piece, that is to say half the length of the large base.

 As seen in Figure 4, these trapezoidal facets are adjacent to four facets 4b, 4c, which converge to the center 01 in the manner of the four facets of a pyramid. This pyramid is truncated by a spherical surface centered on 01 and having the same radius as the spherical surface of the part 2, to form a facet shaped quadrangular spherical cap 4d This cap can be full or receive a central recess, as on the drawing and in this case centrally to this cap 4d, and perpendicular to the lateral facets 4b, extends a flattened foot 4e, this foot 4e widening to present a portion 4f projecting laterally so as to form two extensions in the form of circular sectors 4 having the same radius as the spherical surface 4d centered on 01.

 Referring to FIG. 7, there is seen a piece of vertex 3. The latter has the shape of a diamond-faced parallelepiped, delimiting, from a vertex 3a, coinciding with one of the vertices S1 to S4 of the tetrahedron. The three other facets 3c of the parallelepiped rhombus converge geometrically towards the center 01 in the manner of a pyramid trxanglllaire vertex 01. This pyramid is truncated at a certain distance from the top. theoretical 01 of the diamond opposite the vertex 3a, by a plane perpendicular to the diagonal 01-3a of the rhombus.Enfin, each of the facets 3c has, at its lower part, a relief 3d, whose vertex 3e forms a substantially shaped surface arc of circle, whose radius is equal to the radius of the aforementioned sphere centered on 01. This facet 3d is inclined by about twenty degrees relative to its support 3c to avoid friction with the foot 4e.

 In order to assemble the tetrahedron according to the invention, the top pieces are first put in place, then the lateral pieces which hold them and then the pivot pieces.

It will be understood that in such an assembly, one of the facets 2b of a workpiece 2, for example the workpiece 2 of the face Al, is arranged in a plane parallel to the face A2 and shown in FIG. cleavage, as well as one of the facets 4b of the intermediate part 4 common to the faces A1 and A2, that 1 one of the facets 4c of each of the two lateral elements 4 common to the face A1 and to the face A3, respectively A4, and finally, that one of the facets 3c of the two corner clamps 3 forming the vertices S3 and S4.On accordingly comprises that it is possible to rotate about the axis passing through the vertex S2 , the center 01 and the center of the face A2, according to the arrow of FIG. 1, the assembly formed by the seven pieces common to the face A2 the other pieces of the tetrahedron remaining motionless
Of course, this property is valid for all faces of the tetrahedron During this rotation, the bearings such as 4g and 3e are guided by the corresponding spherical surfaces of adjacent parts, and the cohesion of the assembly is therefore constantly maintained.

 It is then possible to coat the visible faces of the various pieces of lines, drawings and any colorings, so as to attribute to a given face of the tetrahedron, for example Al, the corresponding faces of the pieces 2, 3, 4. Thus, for example, in an extremely simple form, each of the faces A1 to A4 of the tetrahedron may have a different color and the game will consist, from any configuration of the pieces forming the tetrahedron, to bring the pieces back into the position giving each face a uniform color.

 Reference is now made to Figures 8 to 11.

 FIG. 8 shows a schematic view of an octahedral game having six vertices S and eight opposite faces parallel two by two. Thus, four first faces having no common edge are defined and only the first two, A, B, are seen, and four second faces respectively parallel and opposite to the first ones, of which only the last two, G, H, are seen. each of the first faces is formed by the coplanar external facets of four pieces, namely a pivoting part 2 and three vertex parts 5 containing the vertices 5 of the octahedron .-- The pivoting parts 2 of the faces A, B Eroes two other faces of the first series are identical to pieces 2 of the tetrahedron as shown in Figure 3; these parts are rotated as in the tetrahedron, around a central part 1, (not seen in FIG. 8) identical to the core 1 of FIG.

The octahedron thus comprises six pieces 5 each having in its invisible part, the shape of a py stiff and square base (half-octahedron) whose faces are equilateral triangles identical to the equilateral triangles forming the apparent facet of the piece 2. On the other hand, in the non-apparent part of the game, the pieces 5 have the shape of an equal pyramid centered on the geometric center of the octahedron and truncated by a geometric sphere so as to imitate the four facets
Sa and a lower spherical Sb-shaped facet with a central cruusure in the center of which emerges a foot Se which flares at its lower part 5d to present 5th protruding bearing surfaces, these 5th scopes being in built8 with the geometric sphere.

 It is therefore understood that when the crown pieces 5 are mounted on the structure composed of the core and the four pivoting pieces 2, two of the four facets Sa of the crown pieces 5 are pressed against the corresponding facets 2b of the parts 2 and the fifth bearings come to be disposed under the lower spherical facets of the parts 2. In other words, these parts 5 come to cooperate with the pivoting parts 2, in the same way as the pieces 4 in the tetrahedron.

 The four second faces of the octahedron, whose faces G and H are only visible in FIG. 8, consist, on the one hand, of the corresponding apparent facets of the pieces 5 and, on the other hand, by the apparent facet of a part 6 which, unlike the parts 2, is articulated on any axis. This piece 6, above named facial piece, in fact plays the same role as the vertex piece 3 of the tetrahedron, but, on the outside, there is nothing to distinguish it from the pivot pieces 2, so that the player can not identify the pieces. fixed pieces and moving parts of the game and therefore has the impression that all parts are movable.This face piece 6, as shown in Figures 10 and 11 has a pyramid-shaped equilateral triangular base (regular tetrahedron) truncated to form in addition to the apparent facet 6a, three trapezotal facets 6b having the same inclination as the facets 2b of the pieces 2, thus converging towards the geometrical center of the octahedron, and each provided, in the manner of the pieces 3 of the tetrahedron, of reliefs 6c defining circular spans 6d identical to the spans 3e. The lateral facets 6b come into contact with the facets 5a of the parts 5 and the spans 6d come to be arranged under the corresponding spherical facets Sb of the parts 5.

 A number of cleavage or sliding planes having the shape of regular hexagons have thus been made as shown in FIG. 8 and it is understood that it will therefore be possible to rotate in the same position by sliding on such a hexagon cleavage, the assembly constituted by the part 2 of the face B, which piece rotates about its axis of the core 1, the three adjacent pieces of vertex 5 and the three facial pieces 6 having vertexes common with the piece 2. The plane of cleavage passes through the geometric center of the octrahedron and the two sets of parts rotating relative to each other are, externally, rigorously symmetrical.

 With regard to the coloring of the faces, it will be possible, for example, to give two opposite faces the same color, so that each intermediate piece 5 has each of the four colors, it will also be possible to use eight colors or any other process that makes the game as attractive as possible.

 Reference is now made to Figures 12-17.

In these figures, there is shown a spatial logic game in the form of a dodecahedron. Referring more particularly to Figure 12, there is a dodecahedron
having twelve pentagonal faces B1 to B12 of which only six are apparent, namely the faces B1, B2, B4, B6,
B7, B8. each face has five vertices T. The device comprises a central piece or core 7 shown in FIG. 14 and bearing, from a dodecahedral core 7a and on each of the faces of this core in a direction perpendicular to the face, twelve arms 7b which for the rest, are shaped exactly like the arms of the nucleus 1.

 Each face B1 to B12 of the dodecahedron is composed in fact of a pivoting piece 8, five intermediate pieces9 and five top pieces 10. In all, the dodecahedron thus has a core I, twelve central pieces 8, thirty intermediate pieces 9 and twenty pieces of summit 10.

 Referring to Figure 15, we see the shape of a part 8. This has an upper pentagonal apparent facet a from which extend five side facets 8b. The pentagonal prism trunk formed by the faces 8b is cut by a geometric sphere centered on the center of the core 7 and thus forming a concave spherical face 8c opposite to the face 8a.

The center of this concave spherical facet has, like the piece 2 of Figure 3, an arm 8d similar to the arm 2c, this arm carrying a similar extension and allowing its axial connection with one of the arms 7b of the core 7 so as to allow to mount the rotating part 8 about an axis 7b of the core. However, the radial notching, which contained only three notches in the case of the tetrahedron, contains five notches in the case of the dodecahedron.

 Referring to FIGS. 16 to 18, it can be seen that each intermediate piece 9 has the shape of a pyramid with a rectangular base with a vertex 9a, two triangular facets of small angle at the apex 9b and two triangular facets of wide angle at the apex 9c.

The facets 9b are the facets apparent on the faces of the dodecahedron and we see that a part 9 is communicated to two neighboring faces of the dodecahedron, the vertex 9a coming to be arranged in the middle of the common edge of the two faces.

Like the pieces 4 of the tetrahedron and octahedron, the piece 9, which could be solid, is represented in the example described, in hollow form, and the facets 9b, 9, have a certain thickness, for example 2m . It can be seen, moreover, that the facets 9b are interrupted by a return 9d, each return 9d being arranged in a plane parallel to the facet 9b which is not adjacent to it. On the other hand, the facets 9c continue-lower and are interrupted at a distance by being truncated by a geometric sphere centered on the center of the dodecahedron and having the same radius as the geometric sphere of the part 8, so as to form curved returns 9e; in fact, in the example shown, the returns 9d are not really spherical, but cylindrical on a cylinder having the same radius because a certain clearance is allowed between the different parts, because of the elastic assembly of the parts 8, on the core 7, so that the geometric shape of the different parts can be simplified for reasons of manufacturing convenience.

 As in the case of pieces 4 of the tetrahedron and 5 octahedron, inside the room 9, and from the top 9a, extends a foot 9f which ends with an extended sole 9d, having spans curved 9a, the foot being disposed along the plane of symmetry which cuts the faces 9b. In fact, the curved surface 9g which is theoretically the diameter of the aforementioned geometric sphere can be substantially flat for the reasons mentioned above.

 It is therefore understood that when a part 9 is mounted in its position shown in FIG. 12, one of its bearings 9 comes to be disposed under the spherical surface of the part 8, of one of the faces, for example BI, while its other bearing 9 comes to be disposed under the same face of the part 8 of the other face, for example, B6 of the dodecahedron.

Referring to FIGS. 19 to 21, the shape of the top pieces 10 is shown. The part 10, which has a vertex T, comprises, from this vertex T, three identical diametrical facets 10a respectively belonging to the three faces of the dodecahedron which share the same summit
T. The piece 10 is completed by three facets 10b parallel to the faces 10a and thus forming with them a diamond parallelepiped. Each facet 10b has a relief 10c extending from the apex of the parallelepiped opposite the vertex T. These reliefs 10c each have, with respect to the facet 10b which carries it, a bearing surface 10d which, theoretically, would be spherical on the sphere geometric above but in practice, can be flat. We see, in fact, that each relief lOd is connected to the corresponding 1OSD facet, by a triangular connecting surface while the lower facets of the reliefs lOc are, in the figure, all three coplanar, without this being fundamental to the operation Game.

 It is therefore understood that by mounting the crown pieces on the dodecahedron already having, on the core, the pivoting parts 8 and the side parts 9, the bearing surfaces lOd are each arranged under a curved surface 9e of a part 9.

 Therefore, it is understood that when all the parts are mounted, there is, for each face of the dodecahedron, for example the face BI, a sliding plane parallel to this face so that it can be rotated, as shown in FIG. 12, a face BI around the axis of rotation of its part 8, this movement causing the simultaneous rotation not only of the part 8, but five parts 9 adjacent thereto and five pieces of vertex 10 belonging to the same - face.

Of course, it will be necessary to color each face of the dodecahedron obtained. For example, each face could have a specific color, different from the other faces. In a variant that can contribute to the aesthetics of the game and increase the number of achievable figures, while allowing to use only four colors, each face would comprise two colors delimited by two five-pointed stars as in Figure 12, the one having as vertices, the vertices T of the dodecahedron, the other inscribed in the pivoting part 8, the surface portion, grayed in FIG. 12, between the two stars, would be in a first color, the inner and outer portions would be in a second color.Two diametrically opposite faces of the dodecahedron would be such that the first color of one is the second color of the other, and, if the four colors are, for example, yellow, blue, red, green, for do not favor one face compared to others, we will color for example B1 in Blue (first color) and Red (second color)> B2 in Yellow and Green, B4 in
Blue and Green, B6 in Red and Green, B7 in Yellow and Blue and
B8 in Red and Yellow.

 It is understood that a dodecahedral game thus determined allows a very large number of combinations.

 Reference is now made to Figure 22.

 The icosahedron shown has 20 faces C1 to C20> each face consisting of a single piece 13, having an outer facet shaped equi-lateral triangle. This polyhedron also has twelve vertices R and, as we shall see, the five faces having the same common vertex R can rotate around the geometric axis joining the vertex R at the geometric center of the polyhedron. It is therefore understood that it is possible by successive rotations around different vertices to make occupy said faces all possible positions.

 The icosahedron thus represented first comprises in its center, a central piece or core 7 similar to the core 7 of the dodecahedron. The axes of the branches 7a of the core 7 are constantly directed towards a corresponding vertex R of the polyhedron. The icosahedron further comprises twelve internal pivoting pieces 11, having a mushroom shape with a cylindrical foot 11a and a head. The foot lla is intended to be mounted in the corresponding axis 7a to allow the part 11 to be held radially while rotating freely in notched rotation about the corresponding geometric axis. As in the case of the pivoting parts of the three previous solids, the head has an upper spherical facet 11b, opposite the face that carries the foot 11a and five facets 11c These side facets have a concave conical shape according to a geometric cone vertex coinciding with the geometric center of the icosahedron, therefore of the piece 7 and whose axis is the geometric axis passing through that of the arms 7a close to the arm 7a which carries the piece 11, and towards which the lic facet in question is oriented for example 7a for llc.

 Finally, the lld facet which carries the foot 11a is also spherical and forms a surface in the form of a pentagonal ring. The icosahedron also has a plurality of movable inner parts 12, thirty in number, which constitute the intermediate pieces. These parts 12 have a central portion 12a and a peripheral portion 12b fixed to single right with respect to the central portion. As a result, the two end facets 12c and 12d of the portions 12a and 12b protrude from the adjacent portion. The facet 12c is conically convex, or approximatively planar; and the 12d facet is conical concave, on the same geometric cone as the island facets. The internal facet 12k of the part 12a and the peripheral face 12f are each of spherical shape centered on the center of the polyhedron, that is to say the center of the core 7, just like the faces 12R. and lZh, 12 and 12h being on the sphere mummy that 11d, and 12f on the same sphere as llb (with respect to 12k, it is only important that this face is not hindered by the dodecahedron of the core 7 during the pivoting) .

 The 12th longitudinal facets of the parts 12a are conical concave on a cone with the same vertex and axis as the previous one, but wider opening, if possible tangential to the axes 7a which are joined by this piece 12a. The longitudinal facets 12i of the parts 12b are tapered convexly complementary to the facets 11c of the parts 11.

 In the movement about an axis 7a, one of the surfaces 12c will remain close to the axis of rotation, the other will rotate in the cane centered on the axis of rotation and delimited by the five neighboring axes and the five 12th surfaces of the pieces joining these axes. The ideal shape of the corresponding face 12c is therefore conical, in the extension of the face 13e of the outer part 13 (12k is placed against a face 13e of the outer part 13 and the facets ---------- ---------------- 12c at both ends extend the other two 13th). 12d is on the same geometric cone as the facets îlc.

 Finally, the outer pieces 13 which each form a face C1 to C20, have, from their outer equilateral triangle facet, three lateral facets 13a, forming the three faces of a pyramid with an equilateral base, each facet being inclined with respect to the corresponding face C of a theoretical angle of 370221. From each facet 13a extends a convex conical facet 13b such that the top of the geometrical rod passes through the geometric center of the icosahedron and such that the axis of the The cone passes through the vertex R of the triangle (hence the icosahedron) opposite the side of the triangle to which the conical surface is tangent. The axes of these three cones have been materialized in FIG. 25. The three conical facets 13b are truncated by a spherical section forming a peripheral facet 13c in the middle of which extend three new convex conical facets 13d forming a central extension which ends by a thickened part forming three conical 13th facets. The head formed by the three facets 13e and the spherical central facet 13f, is approximately in the form of a three-faceted plateau. The geometrical radius of the sphere forming the facet 13c is equal to the radius of the geometric sphere delimiting the outer surfaces 12f of the parts 12 and the facets 11b of the parts 11.The radius of the spherical peripheral facet 13g is equal to the radius of the geometric sphere determining the portions 12g and 12h and the peripheral facet 11d opposite the facet 11b, and from which extends the axial portion 11a. Finally, of course, the facet 13f is at a distance from the geometric center sufficient to lie outside the central portion of a core 7 as well as the center facet 12k of the part 12.

 The convex conical facets 13d and 13e, respectively, are complementary to the facets 12d and 12e, respectively.

 During the movement (around one of the axes shown in Figure 25), 13d will describe the cone delimited by five faces 12d etcinq faces llc, and 13e will describe the cone delimited by five faces 12e and five axes 7a.

 Advantageously, the parts 13 are made of two separable parts, namely a part comprising the facets 13d and the head 13f and another part comprising the facets 13b and 13a and the visible equilateral outer face, these two parts being capable of to be secured to one another by, for example, snap-fastening.

 For assembly, the inner part of the parts 13 is first placed on the central part and then on the part 12.

Once the various parts 12 and the central part of the parts 13 and put in place, it comes blocking the assembly by putting in place the parts 11. The heads of the parts 11, which cooperate with the 12h scopes parts 12 immobilize these radially so that all parts are mounted. It remains then only to snap on the central part of the parts 13, the peripheral portion of the latter and the icosahedron is then completed. It is understood that there consequently exist four zones delimited by concentric geometrical spheres. The innermost zone is that containing the dodecahedral nucleus of the central part 7. The second zone is that containing the central parts 12a of the moving parts 12 as well as the cylindrical arms 7a extending between the core and the lic heads. It also contains the 13th, 13th heads of the outer parts. The third zone comprises the heads 11c of the parts 11, the parts 12b of the moving parts 12 and the part of the part 13 formed by the three facets 13d. Finally, the fourth zone, the outermost, is entirely formed by the twenty peripheral parts of the parts 13, that is to say the composite parts of the facets 13b, 13a and the outer face in equilateral triangle.

 If, once the icosahedron is fully assembled, the five faces of the same vertex are rotated about an axis joining the geometric center of the core 7 at the vertex considered, the rotation of the head 11 of the inner part will be simultaneously caused. fixed mounting on the corresponding arm 7a, the rotation of the five parts 13 concerned and the rotation of the five parts 12, a face 12c is adjacent to the arm 7a considered. No obstacle prevents the rotation of these five pieces 12 and five pieces 13 considered. These arranged around the arm 7a in question with its head 11, form an assembly whose peripheral surface consists of fragments of cones and spheres participating in movements cone-on-cone and sphere-on-sphere completely free, under the choice of materials makes the friction negligible.

By approximation, it is possible to replace the curved, spherical or conical surfaces with flat surfaces per piece, provided that the cone-on-sphere and sphere-on-sphere motions are respected, and the embroiderings giving the system its cohesion. the connection of the pivoting parts 11 with the core 7, as in the case of other solids, facilitates the pivoting and notching of the parts 7 - allows the system to be immobilized preferentially in the positions where, externally, the icosahedron is reconstituted; in addition, to facilitate gripping, it will be possible to slightly dig the center of the triangular faces to allow the fingers to conveniently place without sliding, these recesses having substantially the same diameter as the holes of a telephone dial.

 The icosahedron can be colored on its outer faces. These can be a puzzle that needs to be reconstructed; but the simplest coloring process seems to be to color not the faces, but the vertices. In other words, the icosahedron is in its final end-of-play position when all the vertices are surrounded by the same color. This means that on each face there are three differently colored areas for example a, b, c (Figure 22) and an uncolored central portion. This can be done by using six different colors for the sectors a, b, c.A given vertex is given an arbitrary color, and to the five nearest vertices the other five colors in an arbitrary order, two diametrically opposite vertices of the icosahedron having the same color. As a result, no vertex is favored over another and two opposite triangles have the same colors for their three angles a, b, c, but are not interchangeable because the colors are not arranged in the same sense. . There is only one solution.

 Of course, here too, the icosahedron could have external faces that would not be flat and triangular. One can imagine to extend towards the outside, each face C1 to C20 of the icosahedron, to give them any relief, for example spherical.

 The last two variants of the invention, which will be called, in the absence of better terminology, the pointed cube and the pointed dodecah, are distinguished from the previous ones in that the external parts, all identical, as in the case of the icosahedron, can be subjected to two kinds of movements: a rotational movement about axes passing through the centers of the faces of the cube and the dodecahedron serving as a support, and a rotational movement about axes passing through the vertices of the cube and the dodecahedron . Therefore, these games are each constituted of a central part of two kinds of pivoting parts, two kinds of intermediate parts and a kind of external parts.

 Figure 27 ---- shows the appearance of the pointed cube, it being understood that the projections, in the form of pyramids in the figure, can be truncated, curved, or any other form respecting the mathematical requirements. explained below. The game has the appearance of a cube, each face of which is divided into four triangles by its two diagonals. To facilitate the understanding of the figures, the diagonals of the faces have been represented by strong lines and the edges of the cube by double lines. Each triangle delimited by two half-diagonals and an edge of the cube constitutes the visible part of an external piece 14 of the game: the game therefore comprises twenty-four identical external pieces. These pieces 14 have, in the figure, an external pyramidal shape. , formed by two facets 14a, grayed out in the figure, resulting in a diagonal and inclined, with respect to the face of the cube, by an angle of 450 maximum, and by a facet 14b, not greyed out in the figure, resulting in an edge and whose inclination relative to the face of the cube is unimportant.

 Figure 28 shows a perspective view of the same pointed cube with schematic separation according to two sliding aan3. We therefore understand by which pivoting it is possible to switch the external parts of the game to bring them into any relative arrangement or bring them back to their original layout: on the one hand, we can rotate 900, 1800 or 2700 the four parts constituting a face of the cube around the axis Al passing through the geometric center O of the cube and the center of the face, (facial pivoting), on the other hand, we can rotate from 1200 or 2400 the six pieces containing a vertex S of the cube, around the axis A2 passing through the geometric center 0 of the cube and the vertex S (diagonal pivoting).

 For this purpose, the central piece 15, shown in FIG. 29, contains fourteen axes resting on the fourteen faces of a cuboctahedron, eight of these axes, 15a, being oriented towards the eight vertices of the cube, and the six others axes, 15b, being oriented towards the centers of the faces; FIG. 29 further shows, in exploded perspective, the two kinds of pivoting parts, 16 and 17, and a kind of intermediate parts, 18. As in the case of the icosahedron, these parts are delimited by spheres and cones participating, during pivoting, to sphere-on-cone and cone-shaped movements, said spheres delimiting two zones, a central zone and an average zone, in which the pivot cones do not have the same opening, which allows the pieces to interlock with each other so that the game does not disassemble during manipulation.

 The facial pivoting part 16 consists of an arm 16a latched on an axis 15b of the center piece.

 trale 15 according to the same method as for the previous descriptions (radial notching four notches), and a head 16b, in t-elm of concave square and curved, whose vertices are directed towards the middle of the edges of the cube of the Figure 27, and which is limited by two spherical facets 16c (convex) and 16d (concave), and four concave facets 16e belonging to cones whose axes are oriented towards the four vertices of the cube face traversed by the axis of the room 16.

 The diagonal pivoting part 17 is also composed of an arm 17a (invisible in FIG. 29), engaged on an axis 15a of the central part 15 directed towards an apex S of the cube, (radial notch with three notches), and a head 17b in the shape of a concave and curved irregular hexagon, whose longest sides are directed towards the diagonals of the faces of the cube according to which the schematic separation of the figure 28 has been carried out. This head is limited by two facets 17c (curved) and 17d (concave) belonging to the same spheres as 16c and 16d respectively, and by six concave facets whose three longer ones, 17f, belong to axes c8nes passing through the geometric center O of the cube and the centers of the faces of the cube containing the vertex S, and whose shorter three, 17th, belong to the cones already containing 16th facets of the three neighboring pieces 16, and whose axes pass through the three vertices of the cube closest to S.

 Between a part 16 of facial pivoting and a piece of diagonal pivoting 17 is an intermediate piece 18, asymmetrical (ax-shaped), composed of a central portion 18a and a middle portion 18b, and which has been redrawn on Figure 30 in a different position, so that we better see the central portion 18a. These two parts 18a and 18b are limited radially by three spherical surfaces, 18c, outer facet of 18b, which belongs to the same sphere as 16c and 17c 18d, contact facet 18a and 18b, belonging to the same sphere as 16d and 17d , so that the ends of 18a protruding from 18b come to get carried away under the facets 16d and 17d when the game is mounted, and 18h, internal facet 18a, obeying the only requirement not to touch the central piece 15 at during the pivoting therefore, for example, to belong to a sphere whose radius is greater than the radius of the sphere circumscribed cuboctahedron of the central piece 15.

 The lateral facets of the part 18 belong to pivoting cones. Thus, the convex facet 18e is in contact with a facet 16 of the pivoting part 16, and therefore belongs to the same cone. The facet 18f, convex and wider than 18th, is in contact with a facet 17f of the pivoting part 17, whereas the facets 18g, concave, each belong to a cone already defined by the facets 16e and 17e of the pivoting parts. 16 and 17. In the most central portion 18a, the convex facets 18i and 18k belong to cones whose axis is respectively the axis of the adjacent piece 16 and the axis of the adjacent piece 17, and tangent to the arm 17a and 16a respectively.Because of the cylindrical shape of the arms 16a and 17a, these cones have a vertex slightly eccentric with respect to the geometric center of the cube, so that a generatrix of the cone is tangent to the cylindrical arm 16a or 17a, so that the facets 18i and 18k are slightly beveled with respect to the spherical facet 18d. The other facets, concave, 181, will belong, in a similar way to a cone whose axis is the same as that of the corresponding facets 18, and whose generator is tangent to the cylindrical arm of the part 16.

 The intermediate piece 19, shown in Figure 31, differs from the piece 18 in that it is symmetrical, because it is located parallel to an edge of the cube, between two parts 17 of diagonal pivoting. Like the piece 18, it is composed of a central part 19a and an average part 19b, radially bounded by three sides 19c, 19d and 19h belonging to the same spheres 78c, 18d and 18h respectively, and laterally limited by channel portions, 19e and 19f each being in contact with a facet 17e of a workpiece 17, while the facets 19g each extend the facets 17f of the same parts 17 in contact; in the inner part 19a, the facets 19i and 19k extend the facets 18i of the nearest parts 18, while the facets 19i, they extend the facets EI of the same parts 18 closest.

 It is therefore understood that the ends of 19a protruding from 19b will be held radially, in the normal position, by the facets 17d of the parts 17; during a diagonal pivoting around one of the parts 17 in contact with the part 19, these ends will be held radially by the facet 18d of a part 18, then by the facet 16d of a part 16, then A-new by a piece 18 to find a normal position in a room 17.

During a facial pivoting, on the other hand, the pieces 19 will remain motionless, and the ends 18a protruding from 18b, ends which, in the normal position, are held by a facet 17d of a part 17, will pass under a facet 19d. of a piece 19 before returning to a new normal position under a facet 17d of another piece 17.

 In the triangle delimited by a piece 19 and two pieces 18 is embedded a part 14, the outer portion will cover all neighboring parts to form the only visible piece when the game is fully assembled. This piece 14, which has already been mentioned in FIGS. 27 and 28, is shown in greater detail in FIG. 32. The two grayened facets 14a and the facet 14b (invisible in FIG. 32) are found forming a pyramid. based on the facet 14c which strictly belongs to the face of the cube. It is this necessity that the facet 14c belongs to the face of the cube (to allow the facial rotation) which forces the piece to be pointed as in the figure, either curved or in the form of a truncated pyramid, so that the cube will never be perfectly cubic externally. The only other mathematical requirement is that the facets 14a are inclined, with respect to 14c, by a maximum angle of 45, without which the diagonal pivoting of neighboring parts is not possible. But outside these two conditions, the outer shape of this piece 14 is completely free.

 The remainder of the piece 14 is delimited by spheres and cones as for the pieces previously described. The facet 14f belongs theoretically to the same sphere as 16c 17c, 18c and l9c, although its spherical character is not fundamental, the facet 14i belongs to the same sphere as the facets 16d, 17d, 18d, l9d, so that the most central part of the part 14 can fit under the middle parts 18b and 19b of the intermediate parts. Finally, the facet 141 belongs to the same sphere as 18h and l9h, although the spherical character of these three facets is not essential.

Laterally, the facets 14d, convex, belong to cones of respective axes OQ and OS, and tangent P to OSP and OQP respectively, so that once the game is assembled, the four pieces of the same face will have at the center P of said face, their facets 14d tangent to each other. The facet 14e, convex, but invisible in Figure 32, is tapered axis
OP and tangent to the OQS plane in the middle of QS. Note that, since the facet 14f is spherical centered at 0, the facet 14e is much higher than the facets 14d at the point P. The facets 14S, convex, are in contact with the facets 18 of the two adjacent pieces 18, while the facet 14h, convex and invisible in Figure 32, is in contact with a facet 19 of the adjacent part 19. In the central part, the facets 14i, convex, are in contact with the facets 18i of the two adjacent parts 18, and the facet 14k, convex and invisible in Figure 32, is in contact with a facet 19i of the adjacent part 19.

 It will be understood that, for assembly, it is necessary that the piece 14 be initially in two pieces, as in the case of the icosahedron: firstly, the inner part of the piece 14 will be mounted, then the intermediate pieces 18 and 19 for radially holding the workpiece 14, then the pivot parts 16 and 17 which radially hold the intermediate parts 18 and 19 and are fixed by snapping to the central part 15, then the outer part of the parts 14, which covers all the parts adjacent, and may be attached to the internal part already in place, for example, by snapping, or by any other method deemed appropriate.

 The pointed cube can be colored, in any way, on its outer faces, so that we can differentiate the external parts. It seems that the simplest method of coloring, using only six colors, consists in attributing to each piece two colors, a facial color on its facets 14a (grayed out in FIG. 27), and a lateral color on its facet 14b. , not shaded in Figure 27. To avoid a face, we will have the six colors for example, as in Figure 33, where the six colors are numbered from 1 to 6. The purpose of the game is then to arrange the pieces not only so that the facial colors of the four pieces of the same face are identical, but in such a way that the lateral colors of the two pieces containing the same edge are also identical: this problem admits only one solution .

 Reference is now made to FIGS. 34 to 38, relating to the dodeca-point.

 The pointed dodecah is very close to the pointed cube, except that it is constructed from a dodecahedron instead of stretcher constructed from a cube, which essentially modifies the external appearance of its pieces and the forms parts of facial rotation. FIG. 34 shows the game once assembled, composed of sixty identical pieces of which only twenty-eight are visible in FIG. 34. FIG. 35 shows the same dodecapointu with schematic separation along two sliding planes, thus illustrating the two possible pivoting, facial rotation (around Al) or diagonal pivoting (around A2).

The outer parts of the dodecapointu, for example ABS, in the form of an isosceles triangle (but not equilateral), have a bolded sides, corresponding to the edge of the dodecahedron serving as a support, and a vertex at the intersection of the axis passing through the geometric center of the dodecahedron and the center of a face of the dodecahedron, and the plane passing through the three vertices A, C, E of the dodecahedron closest to S.Si we choose a dodecahedron whose edge AS is worth 40mu, the other two sides of the triangle
ABS will each be 35mm, the top of the dodecahedron (A or S) will be at a distance of 56mm from the geometric center of the dodecahedron while the third vertex B will be at a distance of 52.6mm from the same geometric center of the cedar dodecah. The angles of the ABS triangle will be mathematically equal to 690 47 'for the B angle, 550 06' for the A and S angles. During a five-piece swivel around the Al axis, an angle of 720, 144 ", 216 or 288", the plane of sliding will cut the solid following a regular pentagon which is no other than a face of the dodecahedron, whereas during a diagonal pivoting of six pieces around the axis A2 passing at the vertex S, at an angle of 1200 or 2400, the plane of slip will cut the solid following an irregular hexagon ABCDEF, whose angles ABC,
CDE, EFA are mathematically equal to 1350 31 ', and whose angles FAB, BCD, DEF are mathematically equal to 104029'.

 The center piece of the dodecapointu, represented in FIG. 36, comprises thirty-two axes coming from the thirty-two faces of the icosidodecahedron, twenty of these axes (axes 20a) being directed towards the twenty vertices of the dodecahedron, and the twelve others (axes 20b), towards the twelve centers of faces of the dodecahedron. The axes 20a are extended by pivoting parts which do not differ fundamentally from the parts 17 of the cuboctahedron (FIG. 29), and of which all the facets play exactly the same role as those of the parts 17 of the cuboctahedron, even if their precise dimensions are slightly The two axes are prolonged by pivoting parts which differ from cuboctahedron parts 16 in that they are pentagonal instead of square (the radial notch is therefore five notches high). ). These pieces are therefore comparable to pieces 11 of the icosahedron (Figure 26). Between a facial pivoting piece 11 and a diagonal pivoting piece 17 is an intermediate piece quite comparable to the piece 18, while between two pieces of diagonal pivoting 17 is parallel to an edge te of the dodecaddre , an intermediate part all-h-fact comparable to the part 19.In the triangle formed by a part 19 and two parts 18 is embedded a part 21, shown in Figure 37, whose facets 21d to 211 play exactly the same role as the facets 14d to 141 of the piece 14 of the pointed cube. Only the facets 21a, 21b and 21c differ. The facet 21a is the only visible from the outside: it is the ABS triangle described above. The facet 21b belongs to a hexagonal sliding plane (ABCDEF), is therefore inclined at a theoretical angle of 11 "26 'with respect to the external facet 21a. The facet Zlc, invisible in FIG. 37, belongs to a plane of sliding pentagonal, therefore to a face of the dodecaddre, and is therefore inclined at a theoretical angle of 16 16 'with respect to the external facet 21a The dimensions mentioned in the text and in Figure 37 may suggest rays of spheres 211, 21i and 21f of 22mm, 29mm and 36mm respectively, Note that the facets 21d are tangent to BA and BS not in B as in the case of the pointed cube, but at a point approximately one third of BA or BS starting from g, so that the facets 21b extend in the neighborhood of B. The facet 21st, it is tangent to AS in the middle.On the other hand, as in the case of the icosahedron and the pointed cube , the piece 21 must be in two pieces in order that the assembly is réa -usable.

 With regard to the coloring of the sixty outer pieces, FIG. 34 suggests, as in the case of the pointed cube, that each piece is marked by two colors, a facial color and a lateral color (shaded parts in FIG. the remainder of the piece being of a neutral color identical for all the pieces (black for example). It can thus be limited to six colors, distributed, as in Figure 38, so that no face is preferred over another, the purpose of the game being to rearrange the pieces so that the five pieces of the same face color, and that the two pieces on both sides of the same edge of the dodecahedron have the same lateral color.This system does not make it possible to differentiate all the pieces, because there are always two pieces with the same facial color and the same lateral color, but trying to differentiate these two parts presents a double risk: on the one hand, to favor one face or orientation of the solid compared to another, on the other hand to make the game too complicated and inaccessible, since the number of theoretically possible combinations is incomparably greater than for the other five games previously described. However, we reserve the possibility of coloring the faces of the dodecapointu in any other way. As in the case of the dodecahedron, it will be wise to slightly recess the center of the room, so as to facilitate gripping and handling.

 The invention has been described with respect to particular embodiments, but it is obvious that it is not limited thereto. Thus, for example, spherical facets and extensions that cooperate with them, could be distributed in reverse. For example, the part 2 could carry extensions instead of a spherical facet 2 and the adjacent part 4 a spherical facet without extensions etc., provided that the assembly of the game remains possible, and that the principle of the movements plan on plane, cone on cone and sphere on sphere be preserved.

Claims (12)

 1 - spatial logic game, characterized in that it is constituted on the basis of a regular polyhedron, selected from the group formed by the tetrahedron, octahedron, dodecahedron and icosahedron or non-regular (pointed cube and dodecapointu), without the external appearance of the solid being necessarily the polyhedron in question, said game having a central piece having equiangular axes, namely extending to the four faces of a regular tetrahedron for the tetrahedron and octahedron , towards the twelve faces of a regular dodecahedron for the dodecahedron and the icosahedron, towards the fourteen faces of a cuboctae dre for the pointed cube, and towards the trend-two sides of an icosidodecahedron for the dodecapointu, each axis bearing a pivoting piece (2, 8, 11) pivotally mounted about said axis (4g, 5, 9g, 12h), intermediate pieces (4, 5, 9, 12) and top pieces (3, 6, 19, 25), the non-visible facets, mutually in contact, of said parts, intended to move relative to each other, being shaped to substantially allow mutual sliding of said parts, radial retaining means being provided to prevent a separation between the central part and the other parts.  2 - Set according to claim 1, characterized in that said retaining means comprise facets (2g, 8c, 11d) of substantially spherical shape or, by approximation, flat, presented by some of the parts (2, 4, 5, 8, 9, 11, 12) and corresponding extensions (4g, 5c, 9s, 12h) presented by the other parts.  3 - Set according to any one of claims 1 and 2, characterized in that the retaining means comprise radial extensions, carried by the parts, and cooperating with circular guide grooves pcrrtcs by the central part, that it being substantially spherical.  4 - Set according to one of claims 1 to 3, formed on the basis of the tetrahedron, characterized in that it comprises, in addition to four pivoting parts (2) and four visible intermediate parts (4), four pieces of vertex (3), said crown pieces having similar radial retaining means, each face of the tetrahedron being constituted by the apparent equilateral triangular facets of the pivoting piece (2), trapezial (4) of the three adjacent pieces (4) and diamond of the three pieces of vertex (3), the non-visible facets in contact with each other (2b, 4b, 4c, 3c) of said parts being flat and respectively parallel to the plane of the face or faces of the tetrahedron which have said parts.  5 - Set according to any one of claims 1 to 3, formed on the basis of an octahedron, characterized in that it comprises, for four non-adjacent faces, each time a pivoting part (2) having a facet apparent in the form of an equilateral triangle, and three adjacent pieces (5) forming apex pieces, the centers of the other four faces being occupied by additional center pieces (6) of the same shape as the pivoting pieces (2) but assembled from non-pivotally, said top pieces (5) having the form of a pyramid with four apparent facets, said pyramids continuing, in the non-visible part, by inverse pyramids truncated by a sphere, the facets (5a) of this truncated pyramid, in contact with the corresponding facets (2b, 6b) of the other parts being respectively flat and parallel each time to a face comprising said apex piece (5).  6 - Set according to 1 any one of claims 1 to 3, formed on the basis of the dodecahedron, characterized in that it comprises twelve pivoting parts, thirty adjacent intermediate parts (9) and twenty pieces of apex (10), each pivoting piece (8) exhibiting a pentagonal outer facet and four inclined lateral facets (8b), each adjacent intermediate piece (9) having the shape of a rectangular base pyramid forming two visible facets (9b) respectively belonging to two adjacent faces of the dodecahedron, and two non-visible faces (9c), each vertex piece (10) having three visible diamonds (1-) facets and three non-visible diamond facets (10b), as well as similar radial retaining means, the non-visible facets of mutual contact of said pieces (8b, Sc, 9d, 10h) being respectively parallel to those of the faces of the polyhedron which comprise a visible facet of the part considered .  7 - Set according to any one of claims 1 to 3, formed on the basis of the icosahedron, characterized in that the twelve equjangular axes are oriented towards the vertices (R) of the icosahedron, that each face of the icosahedron is constituted by the apparent facet of a piece of vertex (13), which it comprises, each time between two consecutive axes of the intermediate intermediate pieces (12) having a first portion (12a) extending between the two axes and a second outermost portion (12b) extending perpendicularly to the first, that the pivoting pieces (11) have a pentagonal shape with substantially spherical radial surfaces (11b, 11d), the innermost surfaces (12a) of the parts (12), said top pieces (13) having a central portion (13e, 13g) coming to be arranged in the interval between three intermediate pieces and a recessed part (13d) coming to be arranged in the gap left by the s alternating uplift of five pivoting pieces (11) and five parts (12a) of the workpiece (12), the mutually contacting facets (11, 11i, 12d, 121, 13e, 13d) having complementary conical shapes on the basis of geometric cones having as geometric center of the dodecahedron and as axis, the axis of pivoting.  8 - Game according to any one of claims 1 to 3, formed from a cube and named "pointed cube" in the description, characterized in that the twenty-four identical external parts can rotate around eight axes oriented towards the tops of the cu be, or about six axes oriented towards the centers of the faces of the cube, which is possible thanks to two types of pivoting parts (16 and 17) integral with a cuboctahedral central part, six pieces of a first type and eight of a second type, and whose head has the shape respectively of a square and an irregular hexagon, concave and curved; It also graces two types of interme- diate parts (19 and 18), some twelve, joining two pieces (17), the other twenty-four, joining a piece (17) and a piece (16), and thanks to a single type of external parts (14), the number of twentyfour, held radially by the intermediate pieces, and which are limited by an edge of the cube and two diagonals of a face of the cube, and are protruding with respect to the faces of the cube on which they rest, all these parts being in contact along spheres delimiting radially a central zone and a mean zone and ensuring the radial retention of parts, and pivoting cones, of which the axes are the axes of the pivoting parts, and whose opening is not the same in the middle zone and in the central zone.  9 - Set according to any one of claims 1 to 3, formed from a dodecahedron and named "dodecapointu" in the description, characterized in that the sixty identical outer parts can rotate about twenty axes oriented towards the dodé-edre vertices, around twelve axes oriented towards the centers of the faces of the dodecahedron, which is possible thanks to two types of pivoting parts (11 and 17) integral with an icosidodecahedral central part, twelve pieces of a first type and twenty pieces of a second type, and whose head has the shape respectively of a regular pentagon and an irregular hexagon, concave and curved thanks also to two types of intermediate pieces (19 and 18), some , thirty in number, joining two pies (17), and the others, sixty, joining a piece (17) and a piece (11), and thanks to a single type of external pieces (21), number of sixty, maintained radially by the intermediate pieces, and which have the external appearance of an isosceles triangle but not equilateral whose largest category is an edge of the dodecahedron on which they rest, all these pieces being in contact along spheres delimiting radially a central zone and a medium zone and ensuring the radial maintenance of the parts, and pivoting cones, whose axes are the axes of the pivoting parts, and whose opening is not the same in the middle zone and in the zone Central.  10 - Game according to any one of claims 7 to 9, characterized in that the parts of its met (13) are made in two parts assembled one central and the other device.  11 - Set according to any one of claims 1 to 10, characterized in that the axes of the central part are materialized by arms (la, 7a).  12 - Set according to any one of claims 1 to 12, characterized in that the outer surface of each piece is colored, the colors being arranged as follows, namely; for the tetrahedron, each face has only one color, ie four colors in all; for the octahedron, each face has only one color, that is, eight colors in all, or two opposite faces have the same color, or four colors in all; for the dodecahedron, each face has two colors delimited by a five-pointed star, the central facet (8) portal, at least partially that of the colors outside the star, two opposite faces of the dodecahedron preferably bearing the same colors but arranged inversely, four colors in all; for the icosa-dancer, the five faces of the same vertex have the same color, or six colors in all; for the pointed cube, a facial color on its facets (14a) and a lateral color on its facet (14b), ie six colors (1 to 6); for the pointed dodecah, each piece is marked by two colors, one facial, the other lateral, the res-te being neutral for all the parts, ie six colors (1 to 6) distributed according to figure 38.