WO1983001008A1 - Hinged solid with four rotation axes - Google Patents

Hinged solid with four rotation axes Download PDF

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Publication number
WO1983001008A1
WO1983001008A1 PCT/FR1982/000155 FR8200155W WO8301008A1 WO 1983001008 A1 WO1983001008 A1 WO 1983001008A1 FR 8200155 W FR8200155 W FR 8200155W WO 8301008 A1 WO8301008 A1 WO 8301008A1
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Prior art keywords
regular
articulated
twenty
parts
fourteen
Prior art date
Application number
PCT/FR1982/000155
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French (fr)
Inventor
Daniel Pecker
Original Assignee
Daniel Pecker
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Daniel Pecker filed Critical Daniel Pecker
Priority to AU89051/82A priority Critical patent/AU8905182A/en
Publication of WO1983001008A1 publication Critical patent/WO1983001008A1/en

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Classifications

    • A—HUMAN NECESSITIES
    • A63—SPORTS; GAMES; AMUSEMENTS
    • A63F—CARD, BOARD, OR ROULETTE GAMES; INDOOR GAMES USING SMALL MOVING PLAYING BODIES; VIDEO GAMES; GAMES NOT OTHERWISE PROVIDED FOR
    • A63F9/00—Games not otherwise provided for
    • A63F9/06—Patience; Other games for self-amusement
    • A63F9/08—Puzzles provided with elements movable in relation, i.e. movably connected, to each other
    • A63F9/0826—Three-dimensional puzzles with slidable or rotatable elements or groups of elements, the main configuration remaining unchanged, e.g. Rubik's cube
    • A63F9/0838—Three-dimensional puzzles with slidable or rotatable elements or groups of elements, the main configuration remaining unchanged, e.g. Rubik's cube with an element, e.g. invisible core, staying permanently in a central position having the function of central retaining spider and with groups of elements rotatable about at least three axes intersecting in one point

Definitions

  • the present invention relates to the use of a system of non-perpendicular axes for the construction of mathematical games of the "articulated solid" type.
  • Solids like this already. known (“Rubik's Cube” and its variants) consist of a regular stack of identical small cubes; this requires taking a system of perpendicular axes and limits the variety of games that can thus be obtained. In addition, all games with a system of perpendicular axes also seem difficult.
  • the axis system according to the invention makes it possible to produce a wide variety of essentially different solids consisting of regular tetrahedra and regular octahedra. These mobile elements are held together by tenons around a system of non-perpendicular axes forming a "regular tetrapod".
  • Figures 1 to 5 describe the application of the axis system to the construction of an articulated truncated tetrahedron.
  • Figures 6 to 10 describe the application of the axis system to the construction of an articulated cuboctahedron.
  • FIGS. 11 to 14 represent several types of articulated solids derived either from the truncated tetrahedron or from the cuboctahedron by addition of elements.
  • Figure 1 describes the part (1): system of four axes arranged in regular tetrapod, that is to say along the four axes of a regular tetrahedron which joins the center of the tetrahedron at the vertices. These hard metal pins are welded together in the center, and their ends are threaded.
  • Figure 2 describes the part (2) which is a regular octahedron of dimension posed on one of its faces called base. It is crossed by a hollow axis perpendicular to the base at its center. It is hollowed out by a sphere of radius r whose center is on the axis at the distance a from the center of the base, (r can be chosen close to a.)
  • Figure 3 describes the part (3) which is a regular tetrahedron on side a, hollowed out by a sphere of radius r whose center is on the right joining the midpoints of two opposite edges, outside the tetrahedron, and at the " distance a from the middle of the edge farthest from the sphere.
  • Two portions of a sphere of the same outer radius r form tenons (of width approximately ) overflowing on either side of the spherical housing thus hollowed out.
  • Figure 4 shows the assembly of the parts of the truncated tetrahedron.
  • the four pieces (2) are threaded onto the axle system (1) with their spherical side facing inwards.
  • the six pieces (3) are inserted, their tenon side inside.
  • the whole being held by four springs (4) threaded on each of the branches of the system of axes (1) and locked on these branches using nuts (5).
  • Figure 5 shows the assembled truncated tetrahedron. This solid, in addition to the parts of the mechanism (1),
  • Figure 6 describes the part (6). It is a regular pyramid of side a, placed on its square base. It is hollowed out by a sphere of radius. Centered at the top of the pyramid (R is approximately equal to aa). We fix in the spherical housing thus formed t on two opposite curvilinear edges, two small tenons which are portions of sphere of the same external radius R.
  • Figure 7 describes the part (7) which is a regular tetrahedron of dimension a, placed on its "base” and hollowed out by a sphere of radius R centered at the top of the tetrahedron. This tetrahedron is crossed by a hollow cylinder of height h (h less than ) whose axis is perpendicular to the base at its center. The upper part of the cylinder is closed by a disc pierced in its center.
  • Figure 8 describes the part (8) which is a regular tetrahedron of side a, hollowed out by a sphere of radius R centered at the top of the tetrahedron. Three portions of a sphere with the same outer radius R, arranged symmetrically, form three tenons.
  • Figure 9 shows the assembly of the cuboctahedron.
  • the four parts (7) are threaded on the axis system (1), spherical faces inward.
  • the six pyramids (6) are interleaved by positioning the tenons inside the tetrahedrons (7). Then we insert the four pieces
  • FIG. 10 represents the assembled coboctaedre, composed of one or two parts of the mechanism, of fourteen moving parts. Other variants derived from the two previous types will now be described.
  • FIG. 11 represents the articulated tetrahedron which is obtained by adding four regular tetrahedra of side a (11), at the four corner of a truncated tetrahedron.
  • Figure 12 describes the oblique cube which is obtained by adding eight identical tetrahedra (12) on each of the eight faces of the cuboctahedron. Each tetrahedron (12) is based on an equilateral triangle with side a and for height .
  • Figure 13 describes the regular octahedron which is obtained by adding six regular pyramids with square base (13) on each of the square faces of the cuboctahedron.
  • Figure 14 describes the star octahedron which is obtained from the cuboctahedron by adding both eight tetrahedra (12) on the triangular faces of the cuboctahedron and six regular pyramids (13) on the square faces of the cuboctahedron.
  • the devices according to the invention can be used for the manufacture of mathematical games according to the embodiments previously described or according to 'equivalents, thus the axes can extend or not, the central part can be hollowed out or not, the male parts can be female and reciprocally.
  • the games can be given the shape of ellipsoid, ovoid, or hemisphere.
  • the variety of possible forms also allows the creation of decorative objects (sulfides).
  • the invention therefore has at least two possible uses! so-called color and shape permutation math games; manufacture of decorative items,

Abstract

A system of non-perpendicular axes is used for the construction of mathematical games of the "hinged solid" type. The embodiment of the Cuboctahedron illustrates this invention: the four tetrahedrons (7) are threaded on the system of axes (1). Pyramids (6) and tetrahedrons (8) are then inserted. Springs (4) and nuts (5) hold together the assembly. Amongst the most interesting application of the invention, there are other hinged solids comprised substantially of stacks of regular tetrahedrons and pyramids.

Description

SOLIDE ARTICULE A QUATRE AXES DE ROTATION. La présente invention concerne l'utilisation d'un système d'axes non-perpendiculaires pour la construction de jeux mathématiques de type "solide articulé". Les solides de ce genre déjà. connus ("Rubik's Cube" et ses variantes) sont constitués d'un empilement régulier de petits cubes identiques; ceci oblige à prendre un système d'axes perpendiculaires et limite la variété des jeux qu'on peut ainsi obtenir. De plus, tous les jeux à système d'axes perpendiculaires semblent également difficiles. SOLID ARTICULATED WITH FOUR ROTATION AXES. The present invention relates to the use of a system of non-perpendicular axes for the construction of mathematical games of the "articulated solid" type. Solids like this already. known ("Rubik's Cube" and its variants) consist of a regular stack of identical small cubes; this requires taking a system of perpendicular axes and limits the variety of games that can thus be obtained. In addition, all games with a system of perpendicular axes also seem difficult.
Le système d'axes selon 1' invention permet de réaliser une grande variété de solides essentiellement différents constitués de tétraèdres réguliers et d'octaèdres réguliers. Ces éléments mobiles sont maintenus entre eux par des tenons autour d'un système d'axes non-perpendiculaires formant un "tétrapode régulier".The axis system according to the invention makes it possible to produce a wide variety of essentially different solids consisting of regular tetrahedra and regular octahedra. These mobile elements are held together by tenons around a system of non-perpendicular axes forming a "regular tetrapod".
A titre d'illustration des dessins sont fournis. Les figures 1 à 5 décrivent l'application du système d'axes a la construction d'un tétraèdre tronque articule.By way of illustration, drawings are provided. Figures 1 to 5 describe the application of the axis system to the construction of an articulated truncated tetrahedron.
Les figures 6 a 10 décrivent l'application du système d'axes à la construction d'un cuboctaèdre articule.Figures 6 to 10 describe the application of the axis system to the construction of an articulated cuboctahedron.
Les figures 11 à 14 représentent plusieurs types de solides articulés dérivés soit du tétraèdre tronque, soit du cuboctaèdre par addition d'éléments.FIGS. 11 to 14 represent several types of articulated solids derived either from the truncated tetrahedron or from the cuboctahedron by addition of elements.
On va maintenant décrire plus en détail le mode de réalisation de la variante relative au tétraèdre tronqué. La figure 1 décrit la pièce (1): système de quatre axes disposes en tétrapode réguliers, c'est àdiré selon les quatre axes d'un tétraèdre régulier qui joignenile centre du tétraèdre aux sommets. Ces axes en métal dur sont soudes entre eux au centre, et leurs extrémités sont filetées. La figure 2 décrit la pièce (2) qui est un octaèdre régulier de cote a posé sur une de ses faces appelée base. Il est traversé par un axe creux perpendiculaire à la base en son centre. Il est évidé par une sphèr de rayon r dont le centre est sur l'axe a la distance
Figure imgf000004_0002
a du centre de la base, (r peut être choisi voisin de a.)We will now describe in more detail the embodiment of the variant relating to the truncated tetrahedron. Figure 1 describes the part (1): system of four axes arranged in regular tetrapod, that is to say along the four axes of a regular tetrahedron which joins the center of the tetrahedron at the vertices. These hard metal pins are welded together in the center, and their ends are threaded. Figure 2 describes the part (2) which is a regular octahedron of dimension posed on one of its faces called base. It is crossed by a hollow axis perpendicular to the base at its center. It is hollowed out by a sphere of radius r whose center is on the axis at the distance
Figure imgf000004_0002
a from the center of the base, (r can be chosen close to a.)
La figure 3 décrit la pièce (3) qui est un tétraèdre régulier de côté a, évidé par une sphère de rayon r dont le centre est sur la droite joignant les milieux de deux arêtes opposées, a l'extérieur du tétraèdre, et à la
Figure imgf000004_0003
" distance a du milieu de l'arête la plus éloignée de la sphère. Deux portions d'une sphère de même rayon extérieur r forment des tenons (de largeur environ
Figure imgf000004_0004
) débordant de part et d'autre du logement sphérique ainsi évidé.Figure 3 describes the part (3) which is a regular tetrahedron on side a, hollowed out by a sphere of radius r whose center is on the right joining the midpoints of two opposite edges, outside the tetrahedron, and at the
Figure imgf000004_0003
" distance a from the middle of the edge farthest from the sphere. Two portions of a sphere of the same outer radius r form tenons (of width approximately
Figure imgf000004_0004
) overflowing on either side of the spherical housing thus hollowed out.
La figure 4 représente l'assemblage des pièces du tétraèdre tronqué . O n enfile les quatre pièces (2 ) sur le système d 'axes (1 ) leur coté sphérique tourné vers l ' intérieur. On intercale les six pièces (3), leur coté tenon à l'intérieur. Le tout étant maintenu par quatre ressorts (4) enfiles sur chacune des branches du système d'axes (1) et bloques sur ces branches à l'aide d'écrous (5). La figure 5 représente le tétraèdre tronque assemble. Ce solide, outre les pièces du mécanisme (1),Figure 4 shows the assembly of the parts of the truncated tetrahedron. The four pieces (2) are threaded onto the axle system (1) with their spherical side facing inwards. The six pieces (3) are inserted, their tenon side inside. The whole being held by four springs (4) threaded on each of the branches of the system of axes (1) and locked on these branches using nuts (5). Figure 5 shows the assembled truncated tetrahedron. This solid, in addition to the parts of the mechanism (1),
(4), (5), est formé dé dix éléments mobiles.(4), (5), is formed of ten mobile elements.
En ce qui concerne la variante relative au cuboctaèdre. La figure 6 décrit la pièce (6). C'est une pyramide régulière de côte a, posée sur sa base carrée. Elle est evidée par une sphère de rayon .centree au sommet de la pyramide (R est environ égal a a ). On fixe dans le
Figure imgf000004_0001
logement sphérique ainsi formé t sur deux arêtes curvilignes opposées, deux petits tenons qui sont des portions de sphère de même rayon extérieur R. La figure 7 décrit la pièce (7) qui est un tétraèdre régulier de cote a,posé sur sa "base" et évidé par une sphère de rayon R centrée au sommet du tétraèdre. Ce tétraèdre est traversé par un cylindre creux de hauteur h (h inférieur a
Figure imgf000005_0002
) dont l'axe est perpendiculaire à la base en son centre. La partie supérieure du cylindre est obturée par un disque perce en son centre.Regarding the variant relating to the cuboctahedron. Figure 6 describes the part (6). It is a regular pyramid of side a, placed on its square base. It is hollowed out by a sphere of radius. Centered at the top of the pyramid (R is approximately equal to aa). We fix in the
Figure imgf000004_0001
spherical housing thus formed t on two opposite curvilinear edges, two small tenons which are portions of sphere of the same external radius R. Figure 7 describes the part (7) which is a regular tetrahedron of dimension a, placed on its "base" and hollowed out by a sphere of radius R centered at the top of the tetrahedron. This tetrahedron is crossed by a hollow cylinder of height h (h less than
Figure imgf000005_0002
) whose axis is perpendicular to the base at its center. The upper part of the cylinder is closed by a disc pierced in its center.
La figure 8 décrit la pièce (8) qui est un tétraèdre régulier de côté a, evide par une sphère de rayon R centrée au sommet du tétraèdre. Trois portionsd'une sphère de même rayon extérieur R, disposées symétriquement, forment trois tenons.Figure 8 describes the part (8) which is a regular tetrahedron of side a, hollowed out by a sphere of radius R centered at the top of the tetrahedron. Three portions of a sphere with the same outer radius R, arranged symmetrically, form three tenons.
La figure 9 représente l'assemblage du cuboctaèdre.Figure 9 shows the assembly of the cuboctahedron.
Les quatre pièces (7) sont enfilées sur le système d'axes (1), faces spheriques vers l'intérieur. On intercalle les six pyramides (6) en pos.itionnant les tenons a l'intérieur des tétraèdres (7). Puis on intercalle les quatre piècesThe four parts (7) are threaded on the axis system (1), spherical faces inward. The six pyramids (6) are interleaved by positioning the tenons inside the tetrahedrons (7). Then we insert the four pieces
(8) dans les espaces restes vacants. Le tout étant maintenu par des ressorts (4) enfiles sur la pièce (1), enfonces dans les cylindres des pièces (7) et fixes par des ecrous (5).(8) in the remaining vacant spaces. The whole being maintained by springs (4) threaded on the part (1), pressed into the cylinders of the parts (7) and fixed by nuts (5).
La figure 10 représente le coboctaedre assemble, compos sii o ouuttrree 1l'es pièces du mécanisme, de quatorze pièces mobiles. D'autres variantes dérivées des deux types précédents vont maintenant être décrites.FIG. 10 represents the assembled coboctaedre, composed of one or two parts of the mechanism, of fourteen moving parts. Other variants derived from the two previous types will now be described.
La figure 11 représente le tétraèdre articule qu'on obtient en rajoutant quatre tétraèdres réguliers de coté a (11), au quatre coin d'un tétraèdre tronque. La figure 12 décrit le cube oblique qui s'obtient en rajoutant huit tétraèdres identiques (12) sur chacune des huit faces du cuboctaèdre. Chaque tétraèdre (12) a pour base un triangle equilateral de côté a et pour hauteur
Figure imgf000005_0001
. La figure 13 décrit l'octaèdre régulier qui s'obtient en rajoutant six pyramides régulières a base carrée (13) sur chacune des faces carrées du cuboctaèdre. La figure 14 décrit l'octaèdre étoile qui s'obtient a partir du cuboctaèdre en rajoutant à la fois huit tétraèdres (12) sur les faces triangulaires du cuboctaèdre et six pyramides régulières (13) sur les faces carrées du cuboctaèdre.FIG. 11 represents the articulated tetrahedron which is obtained by adding four regular tetrahedra of side a (11), at the four corner of a truncated tetrahedron. Figure 12 describes the oblique cube which is obtained by adding eight identical tetrahedra (12) on each of the eight faces of the cuboctahedron. Each tetrahedron (12) is based on an equilateral triangle with side a and for height
Figure imgf000005_0001
. Figure 13 describes the regular octahedron which is obtained by adding six regular pyramids with square base (13) on each of the square faces of the cuboctahedron. Figure 14 describes the star octahedron which is obtained from the cuboctahedron by adding both eight tetrahedra (12) on the triangular faces of the cuboctahedron and six regular pyramids (13) on the square faces of the cuboctahedron.
Les dispositifs suivant l'invention peuvent être utilises pour la fabrication de jeux mathématiques selon les modes de réalisation précédemment décrits ou selon des 'équivalents, ainsi les axes peuvent déborder ou non, la partie centrale être evidee ou non, les pièces mâles peuvent être femelles et réciproquement.The devices according to the invention can be used for the manufacture of mathematical games according to the embodiments previously described or according to 'equivalents, thus the axes can extend or not, the central part can be hollowed out or not, the male parts can be female and reciprocally.
De plus, par fixation de petits morceaux supplémentaires, on peut donner aux jeux des formes d'ellipsoïde, d'ovoïde, ou d'hémisphère. La variété des formes possibles permet également la réalisation d'objets de nature décorative (sulfures). L'invention a donc au moins deux utilisations possibles! jeux mathématiques dits de permutation de couleurs et de formes; fabrication d'objets à usage décoratifs, In addition, by fixing additional small pieces, the games can be given the shape of ellipsoid, ovoid, or hemisphere. The variety of possible forms also allows the creation of decorative objects (sulfides). The invention therefore has at least two possible uses! so-called color and shape permutation math games; manufacture of decorative items,

Claims

REVENDICATIONS..CLAIMS ..
i) Solide articulé composé d'éléments mobiles autour d'un système d'axes rigides, caractérisé par le fait que les éléments mobiles, maintenus entre eux par des tenons, sont six octaèdres réguliers(6) et huit tétraèdres réguliers (7) (S), les quatre tétraèdres (7) sont enfilés sur un système d'axes non-perpendiculaires formant un "tétrapode régulier" (1),1e tout constituant un "cuboctaèdre régulier" à quatorze pièces mobiles. 2) Solide articulé selon la revendication 1 caractérisé en ce qu'il comporte huit tétraèdres supple mentaires (12) solidaires ou non des pièces (7) (S) sur lesquelles ils sont en appui, le tout constituant un cube articulé possédant quatorze ou vingt-deux pièces mobiles. 3) Solide articulé selon la revendication 1 caractérisé en ce qu'il comporte six pyramides régulières supplémentaires (15) solidaires ou non des pièces (6) sur lesquelles elles sont en appui, le tout constituant un octaèdre régulier à quatorze ou vingt éléments mobiles. 4) Solide articulé selon la revendication 3 caractérisé en ce qu'il comporte huit tétraèdres supplémentaires (12) solidaires ou non des pièces (7)et(8) sur lesquelles ils sont en appui, le tout constituant un octaèdre régulier "étoile" ayant quatorze,vingt, vingt-deux ou vingt-huit pièces mobiles.i) Articulated solid composed of mobile elements around a system of rigid axes, characterized in that the mobile elements, held together by tenons, are six regular octahedra (6) and eight regular tetrahedra (7) ( S), the four tetrahedra (7) are threaded on a system of non-perpendicular axes forming a "regular tetrapod" (1), the whole constituting a "regular cuboctahedron" with fourteen moving parts. 2) articulated solid according to claim 1 characterized in that it comprises eight additional tetrahedrons (12) integral or not with the parts (7) (S) on which they are supported, the whole constituting an articulated cube having fourteen or twenty -two moving parts. 3) articulated solid according to claim 1 characterized in that it comprises six additional regular pyramids (15) integral or not with the parts (6) on which they are supported, the whole constituting a regular octahedron with fourteen or twenty movable elements. 4) articulated solid according to claim 3 characterized in that it comprises eight additional tetrahedra (12) integral or not with the parts (7) and (8) on which they are supported, the whole constituting a regular octahedron "star" having fourteen, twenty, twenty-two or twenty-eight moving parts.
5) Solide articulé selon l'une quelconque des revendications précédentes caractérisé en ce que les evidements et les tenons sont de forme sphérique.5) articulated solid according to any one of the preceding claims, characterized in that the recesses and the pins are of spherical shape.
6) Solide articulé selon les revendications 1,2,3, + caractérisé en ce que les evidements et les tenons sont de forme cylindrique. 6) articulated solid according to claims 1,2,3, + characterized in that the recesses and the pins are of cylindrical shape.
PCT/FR1982/000155 1981-09-24 1982-09-23 Hinged solid with four rotation axes WO1983001008A1 (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
AU89051/82A AU8905182A (en) 1981-09-24 1982-09-23 Solide articule a quatre axes de rotation

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
FR8117984A FR2513138A1 (en) 1981-09-24 1981-09-24 ARTICULATED SOLID COMPOSED OF MOBILE ELEMENTS AROUND A NON-PERPENDICULAR AXIS SYSTEM FOR USE AS A GAME OR A DECORATIVE OBJECT
FR81/17984810924 1981-09-24

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FR (1) FR2513138A1 (en)
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
GB2269760A (en) * 1992-08-17 1994-02-23 Uwe Meffert Logical puzzle

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107261483A (en) * 2017-08-04 2017-10-20 张英仁 Intelligent magic box

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP0042695A2 (en) * 1981-03-27 1981-12-30 Uwe Meffert Puzzle toy
FR2491346A1 (en) * 1980-10-03 1982-04-09 Politechnika Ipari Szovetkezet

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
FR2491346A1 (en) * 1980-10-03 1982-04-09 Politechnika Ipari Szovetkezet
EP0042695A2 (en) * 1981-03-27 1981-12-30 Uwe Meffert Puzzle toy

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
GB2269760A (en) * 1992-08-17 1994-02-23 Uwe Meffert Logical puzzle
US5358247A (en) * 1992-08-17 1994-10-25 I-Development Institute Ltd. Puzzle ball
GB2269760B (en) * 1992-08-17 1996-01-24 Uwe Meffert A puzzle

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FR2513138A1 (en) 1983-03-25

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