FR2515972A1 - Three-dimensional logic puzzle - has spherical surface with polygons sliding along planes orthogonal to axes and held by studs - Google Patents

Abstract

The puzzle is a sphere whose surface is subdivided into spherical surface movable polygons. The polygons are held on a central sphere and can pivot about axes, passing through the centre of the sphere, along planes that are orthogonal to the axes. The polygons are held together by studs on one edge fitting into corresponding grooves in the edge of the next piece. These can be arranged in tiers and the joining pieces can be symmetrical or in the form of mobile or semi-fixed slides.

Description

THIRD PATIENCE CONSISTING OF A SPHERE OR A REGULAR VOLUME HAVING PERMUTABLE SURFACE ELEMENTS.

The invention relates to a logic game consisting of an object of spherical shape whose surface is subdivided into a plurality of mobile spherical polygons, some of the polygons being identical.

 It is possible with the help of constructive arrangements, which will be described later, to obtain, by a succession of rotations around intersecting axes, permutations between elements or moving parts constituting the surface of a sphere or of certain volumes. regular.

The game consists, after having scrambled the initial order of the pieces, materialized by drawings, colored areas, figures or any other mode of identification, to reconstitute this initial order in the minimum of time and if possible with the minimum of maneuvers .

The conditions for such an object to be realizable are multiple and we will examine them in the case of the sphere, which constitutes the regular volume par excellence. The sphere has the peculiarity of having a perfectly continuous surface on which the permutations appear as the surprising result of successive sliding comparable to a kind of continental drift. One could also compare these permutations to those of a curious teasing that would be closed on itself and would not include an empty box.

The first condition of feasibility is that the cut-out makes appear some identical pieces so that there are indeed permutable objects The second condition is that the axes around which the rotations take place pass by the center of the sphere in order to keep intact the shape of it. The rotating zone and the fixed zone will therefore always be separated on the surface of the sphere 1 by a circle 2 located in the partition plane 3 orthogonal to the axis of rotation 4 (FIG 1) .Several axes of rotation will therefore determine several intersecting circles on the surface of the sphere and it will result that the pieces thus obtained (fig 2) will be spherical polygons - bigones or spindles - trigons or spherical triangles tetragon or squares - rectangles - pentagonal spherical trapeziums ..., that we will henceforth designate one of these terms. The third condition is that one manages to mechanically maintain the parts between them while allowing freely the rotations of certain zones, always comprising several parts, compared to the rest of the sphere.

To realize the first condition the number and the disposition of the axes can not be any:
We have already seen that the second condition requires that the axes are concurrent in the center of the sphere; they must also be arranged in line with each other with a certain regularity so that the pieces determined by the sharing plans may include identical groups. There are basically two kinds of satisfactory regularities - the axes are coplanar (all situated in the same plane) and form between them equal angles, like the spokes of a wheel for example. To this first type of solution can be associated an axis perpendicular to the plane of the wheel, that is to say coinciding with the axis thereof.

The axes are distributed regularly in the space so that the angles formed by any two adjacent axes are equal. The axes thus cross the surface of the sphere at points equidistant from all their neighbors and corresponding to the centers of the faces of the regular polyhedrons which admit this sphere as inscribed sphere: hexahedron (3 axes), octahedron (4 axes), dodecahedron ( 6 axes), iscocahedron (10 axes). To this family it is necessary to add certain possibilities of combinations which preserve the regularity necessary to obtain identical parts: nesting solutions with 3 and 4 axes for example.

A number of satisfactory arrangements of the pivot axes are described in Table 1.

Still to satisfy the condition of existence of identical parts sharing plans can not be arranged in any way. In many cases they will have to go through the center of the sphere and we will call them "diametral" or "equatorial" since they share the sphere in two hemispheres. This is true for all solutions with coplanar axes and for sharing plans corresponding to them.

On the other hand, when the axes cross the surface of the sphere in the center of pieces which then constitute pivots, it is no longer necessary for the sharing planes to be equatorial. If they are not half of the pivots will be of the same shape but larger in size than other half. Finally, there is a third possibility of sharing plans, which consists of splitting them symmetrically with respect to the equatorial plane. Vis-à-vis the corresponding axis 4 there appear three zones 5, 6 and 7 can rotate relative to each other (Figure 3). An area 5 that can be designated median, or equatorial, or tropical and two polar zones 6 and 7.

Of course, to perform a maneuver must immobilize two areas relative to the third which is a little less easy than rotate one hemisphere relative to the other; however, this maneuver remains easy because it is sufficient to hold the middle zone with one hand and to rotate a polar zone with the other hand. We can think of more than two parallel sharing plans but the maneuvers become difficult. The most satisfactory arrangements are grouped in Table 1 where we specify the number and shape of the parts obtained, and which refers to the appended drawings. , in which Figures 1, 2 and 3 show different planes of sharing a sphere described above;
Figure 4A is an elevational and plan view of a sphere according to the invention, with two orthogonal axes of rotation; Figures 4B to 4H are views similar to those of Figure 4A, illustrating different embodiments; Figs. 5 are fragmentary views of a sphere according to the invention showing different methods of assembling double-effect rabbet edges; FIGS. 6 and 7 are views similar to those of FIG. 5, showing single-acting rebates and stepped rebates, respectively; Figures 8 illustrate other variants of assemblies according to the invention; Figure 9 is an exploded perspective view of a set according to the invention with polygons held on an intcrne sphere; Figure 10 is a sectional view on the left side and in elevation on the right side. of a game according to the invention ,. four coplanar axes and an orthogonal axis; Figure 11 shows in plan, partially in section, and in elevation a four-axis sphere regularly distributed in space; Figure 12 shows in half section and in elevation a sphere with three orthogonal axes.

Table 1

<tb> DisBosition <SEP> of <SEP> axes <SEP> of <SEP> rotation <SEP> and <SEP><SEP> form of <SEP> pieces <SEP> obtained
<tb> Case <SEP> Figure <SEP> Number <SEP><SEP> Layout of <SEP><SEP> Figures Obtained <SEP><SEP> Lengths of
<tb><SEP> axes <SEP> axes <SEP> pieces <SEP> in <SEP> degree
<tb> A <SEP> 4A <SEP> 1 <SEP> 2 <SEP> orthogonal <SEP> 4 <SEP><SEP> spindles of <SEP> 900 <SEP> 1800 <SEP>
<tb><SEP> to <SEP> the equator
<tb> B <SEP> 48 <SEP> 3 <SEP> coplanar <SEP> to <SEP> 4 <SEP><SEP> spindles of <SEP> 600 <SEP> 1800
<tb><SEP> 60
<tb> C <SEP> 4C <SEP> N (1) <SEP> coplanar <SEP> to <SEP> 2 <SEP> N <SEP> spindles <SEP> of <SEP> 180
<tb><SEP> 180 / N <SEP> 180 / N <SEP>
<tb> D <SEP> 4D <SEP> N + 1 <SEP> N <SEP> coplanar <SEP> 4 <SEP> N <SEP> half-spindle <SEP> 900
<tb><SEP> + <SEP> 1 <SEP> orthogonal <SEP> of <SEP> 180 / N <SEP>
<tb> E <SEP> 4E <SEP> N + 1 <SEP> id. <SEP> D <SEP> but <SEP> 2 <SEP> 4 <SEP> N <SEP> trigones <SEP> iso <SEP> depend on <SEP> of <SEP>
<tb><SEP> plans <SEP> of <SEP> by <SEP><SEP> polar <SEP> distance <SEP> between
<tb><SEP> tage <SEP>"tropical"<SEP> + <SEP> 2 <SEP> N <SEP> tetragones <SEP> plans
<tb><SEP> Tropical
<tb> F (2) <SEP> 4F <SEP> 3 <SEP> orthogonal <SEP> 8- <SEP> trigones <SEP> rec- <SEP> 900
<tb><SEP> tangles <SEP> equilateral
<tb><SEP> raux
<tb> G <SEP> 4G <SEP> 3 <SEP> orthogonal <SEP> 6 <SEP> tetragone <SEP> squares <SEP> depend <SEP> of <SEP>
<tb><SEP> all <SEP> the <SEP> plans <SEP> of <SEP> 12 <SEP> ... <SEP> rectangles <SEP> distance <SEP> between
<tb><SEP> shares <SEP> are <SEP><SEP> 8 <SEP> trigones <SEP> equals <SEP> plans
<tb><SEP> double <SEP> tér
<tb> H <SEP> 4H <SEP> 4 <SEP> regularly <SEP> 8 <SEP> trigones <SEP> equals <SEP> 600
<tb><SEP> Distributed <SEP> (SEP Axes)
<tb><SEP><SEP> faces <SEP> of <SEP> 6 <SEP> tetragones <SEP> squares
<tb><SEP> the octahedron <SEP> regu
<tb><SEP> link)
<tb> I <SEP> 6 <SEP> regularly <SEP> 12 <SEP> pentagons <SEP> 360
<tb><SEP> distributed <SEP> 20 <SEP> trigones <SEP> equi
<tb><SEP>(<SEP> axes of <SEP> lateral <SEP> faces
<tb><SEP> of the <SEP> dodecahedron
<tb> 3 <SEP> 7 <SEP><SEP> combination of <SEP> 8 <SEP> trigones <SEP><SEP> 60
<tb><SEP> 3 <SEP> 3 <SEP> and <SEP> 4 <SEP> axes <SEP> im- <SE>
<tb><SEP> bricks <SEP> 24 <SEP> trigones <SEP> rec- <SEP> 600 <SEP> x <SEP> 45 <SEP> x <SEP> 45
<tb><SEP> tangles <SEP> isosceles
<tb> K <SEP> 10 <SEP><SEP> axes of <SEP> iso <SEP> (for <SEP> memory)
<tb><SEP> cedar
<tb> (1) N can theoretically be any (2) This solution belongs to both the first family since it
has two coplanar axes with an orthogonal axis
and to the second family of axes regularly distributed in space.

 It is useless to comment in detail on Table 1, which summarizes different arrangements of the pivot axes and the shapes of the polygons or parts obtained, and it suffices to recall that the realization of such a spherical object supposes that we know how to solve the problem. maintaining the parts together while allowing rotations around the various axes. The technological solutions may be highly dependent on the different cases considered in Table 1 and will be the subject of the following claims: 1. Double-effect rabbets.

This claim relates to a retaining device designated "double-action rebates" which alone allows two adjacent parts to be secured to all the directions of effort which tend to separate them, but which freely authorizes their relative displacement. along the axis of the circle that separates them. This device requires that the edges in contact of the two parts to be maintained between them are differentiated; For convenience, we will say that one of the borders 8 will have to be male and the other 9 female. FIG. 5 gives a certain number of nonlimiting examples of embodiments of such rebates. When hooks 10 are used, they must be integral with one of the parts or entrained by it. This type of rabbet is usable whenever during maneuvers there is always a male edge opposite a female border, regardless of the permutations made between pieces. This rule is valid for example in the following cases: - B - C, when N is odd - E, for the only tropical links - G - H. To allow the mounting some male and / or female rabbets or hooks may present elasticity.

2. Single-effect rabbets.

When it exists to keep the two parts in contact with a device other than the opposite grooves, "single-action rebates" may be used. They no longer have to maintain the parts against forces that tend to separate them but to ensure that the edges remain perfectly face to face and do not risk derailing. Figure 6 gives some non-limiting examples. In order to prevent certain pieces from falling inside the sphere, it may be made use of an inner sphere 11 on which the piece 9 can bear while sliding freely. As the double-acting rabbets a male border must always be opposite a female border and the cases of application are therefore similar to the reserve near the existence of a device for keeping the parts in contact.

3. Stepped rebates.

When the opposite borders change Ge genre from one piece to the next along the same side of one of the sharing plans one can no longer make use of simply male borders on one side and females on the other, In some In this case, with at least three groups of pieces, it will be possible to make use of curbs with several staggered rebates, the type of which may differ according to the level.

Figure 7 gives two examples, single and double-acting. Type 12 pieces are male for the upper rabbet, females for the lower. Type 13 coins have their inverted genres. Type 14 pieces are female only. We find that 12 and 13 are compatible as well as 12 and 14, 13 and 14. Only parts of the same type are not compatible with each other; if they are never in the presence this type of rabbets can be used. Case I is an excellent example: half of the pentagons can be of type 12, the other half of type 13 and the triangles of type 14. It is obviously possible to multiply the number of staggered rebates to solve more compatibility problems. complex.

4. Undifferentiated or asymmetrical leaves.

Another way to solve the compatibility problems between borders whose parity varies, is to use undifferentiated edges, that is to say, symmetrical, or more precisely, identical. It is then necessary to necessarily make use of connecting pieces whose main problem will be to prevent them from being positioned incorrectly at the crossroads of two dividing lines and thus block certain possibilities of movement.

FIG. 8 gives an example of single-bead rebates which also provide the advantage of great maneuverability. The balls may be replaced by rollers 15 or better by sprockets 16 meshing on rims provided with racks. The gears performing along the dividing line a linear displacement that is exactly half d; Relative displacement of the two zones in presence, there will never be a risk of shift and we can arrange the sprockets at the start so that they never block the movements. In addition, their number can be reduced since they always remain perfectly equidistant. The pinions can cause the retention of slides 17 ensuring the maintenance of the two undifferentiated edges vis-à-vis the separation efforts to constitute double-action rabbets of which use then becomes absolutely universal. In contrast to these movable slides, it is possible to use semi-fixed slides 18, the particularity of which is to allow the free sliding of the parts which they join, whereas they remain fixed with respect to a permanent reference system. each time the rotation is made along their line of partition. We can also say, which amounts to the same thing, that they are sometimes in solidarity with one of the pieces they gather and sometimes with the other, hence the name of semi-fixed that we give them. can be obtained for example by means of rockers 19 secured slides 18.

Bosses 20 belonging to a sphere or rigid inner part 21, which then serves as a reference system and must be joined to at least one of the parts of the sphere, ensure in each stop position the engagement of the rocker in a housing 22 belonging to one of the two pieces joined by the slide. The choice of this piece depends on the site and is such that this piece remains motionless vis-à-vis the reference system while the other can move freely during a movement along the dividing line between them . It is also possible to immobilize the slideways 18 of simple fixed stops 20 'which are solid with the piece 21. These stops 20' can be located at the poles when it is a question of meridian slides, as in the cases B, C, D, E for example.

5. Grooved systems.

It is also possible to maintain the parts by means of an inner sphere 22 secured to one of the parts 23 and having grooves 24 (FIG 9). Each movable piece then has a keel-shaped protrusion 25 directed towards the center of the sphere and whose head can engage in the grooves of the inner sphere. The piece is thus pressed against the sphere and guided in its movements. It is oriented by the adjacent parts which, step by step, rest on the borders of the reference part 23. Conversely, the grooves can be made in the inner face of the moving parts and the pins integral with the part Central. If the inner sphere is not integral with one of the parts then it must serve as a pivot to at least two parts crossed at their center by two pivot axes.

In order to illustrate some of the claims that have just been stated, we will give three exemplary embodiments of spheres with five, four and three-axis permutable pieces.

A) Five-axis sphere
The first example (FIG 10) is that of a sphere with four coplanar axes and an orthogonal polar axis 26 associated. With respect to this axis there are two sharing plans ("tropical") 27. The meridian rebates are of the "pinion slide" type Each slide 28 has two pinions 29 so that when passing a pinion at the poles or at intersections with the tropical planes, where the racks must be interrupted, the synchronism remains assured. The tropical rabbets are of the double-acting type and have elastic hooks 30 which allow the final assembly.The marking mode shown is that of a series of twenty-four digits succeeding each other on three superimposed circular lines. The game consists, as with a tease, in restoring the natural sequence of numbers after having scrambled their initial order.With twenty-four digits the number of possible combinations exceeds ten billion Billion, which means that the restoration of the initial order can only be obtained using an already elaborate methodology, with three coplanar axes instead of four The number of coins is reduced to eighteen and the game becomes more accessible to ordinary mortals. Of course, the cutting mode lends itself particularly well to a "land globe" type of landmark. The game, particularly educational, is then to properly put in place the continents.

B) Four-axis sphere:
The second example (FIG 11) is that of a sphere with four axes 31, 32, 33, 34 regularly distributed in the space; 31 is vertical, 32, 33, 34 oblique. The axes passing through the centers of the eight triangles it is possible to join four of them 35, 36 (37 and 38 are hidden) to an inner sphere 39 which serves-pivot, through axes 40, and ensures their maintaining a fixed distance from the center of the sphere. Under these conditions, single-effect rebates can be used. The four pivot triangles have for example all their male rabbets, the other four triangles 41, 42, 43, 44 all their female rabbets and the six spherical squares 45 have two opposite rabbets females and the other two males.

It is easy to see that, regardless of the movements made, the parity of the rabbets in the presence remains respected. The registration can be for example of the globe type. The reinstatement of the fourteen pieces is an educational game relatively accessible to all.

C) Three-axis sphere
The third example (Fig. 12) is that of a sphere with three orthogonal axes. The sharing plans 46 are all split giving six squares, twelve rectangles and eight triangles. The location shown is that of six spherical caps of different colors symbolized in the figure by separate hatching. The six squares are unicoloured, the twelve two-colored rectangles and the eight triangles are tricolor. The number of combinations is comparable to that of the first example and the restoration of the initial order therefore requires a certain method. The example is shown with double-acting rebates made directly by molding in plastic parts having a slight elasticity to allow mounting. This example is distinguished by its great simplicity and the fact that the interior of the sphere is totally empty. As in the second example, it is easy to see that the parity of the rabbets in the presence is respected in all positions.

The invention is of course in no way limited to the modes of implementation more particularly described and represented.

Claims (10)

claims A logic unit consisting of an object of spherical shape whose surface is subdivided into a plurality of mobile spherical polygons (35, 36, 42 to 45), some of the polygons being identical, characterized in that it comprises holding means (8-20) said polygons to maintain these on said surface, the shape of said polygons and said holding means being arranged to allow pivoting of said polygons around several intersecting axes (31, 32, 33, 34) in the center of the sphere, along sharing planes orthogonal to said axes. 2. 3.eu according to claim 1, characterized in that it comprises concurrent coplanar pivoting axes of said polygons, N being an integerS said axes forming between them equal angles and the spherical polygons being spindles. 3. 3eu according to claim 2, characterized in that it further comprises an orthogonal pivot axis (26) to said coplanar axes defining equatorial sharing planes, tropical or parallel to the plane containing said coplanar axes. 4. 3eu according to claim 1, characterized in that it comprises several concurrent axes regularly distributed in space, the angles formed by two neighboring axes being equal and their arrangement similar to that of the orthogonal axes to the faces of a regular polyhedron . 5. Game according to any one of the preceding claims, characterized in that said holding means comprise guide means (8 to 16) extending along the circular borders opposite said polygons to maintain said borders facing face while allowing free sliding along the arc of polygon separation. 6. 3eu according to claim 5, characterized in that the holding means comprise double-action rabbets (8, 9, 10) formed on the opposite edges, one edge being male and the other female to secure said borders opposite by allowing only free sliding along the arc of polygon separation circle. 7. Game according to claim 5 or 6, characterized in that the holding means comprise step rebates (12, 13, 14) formed on said borders and whose gender differs according to the level. 8. 3eu according to claim 5 or 6, characterized in that the holding means comprise rebates (15, 16) undifferentiated or symmetrical and connecting pieces in the form of slides (17, 18, 19) movable or semifixes liaison said movement-controlled borders to Never block the movements of said polygons. 9. Game according to any one of claims 1 to 4, characterized in that said holding means comprise an inner sphere of said polygons support and connecting means (24, 25) of the polygons (23) to said sphere arranged for allow the polygons to slide over the sphere along the sharing planes. 10. 3eu according to any one of the preceding claims, characterized in that it comprises four intersecting coplanar axes defining 8 spindles of 450 and a polar orthogonal axis (26), the latter axis defining two planes of tropical division of the spindles, said polygons comprising 16 polar isosceles trigones (27 to 30) allowing only relative slides according to the sharing planes.