GB2101491A

GB2101491A - Dodecahedron puzzle

Info

Publication number: GB2101491A
Application number: GB8207901A
Authority: GB
Inventors: Helmut Corbeck; Christoph Bandelow
Original assignee: Arxon Spiel & Freizeit GmbH
Current assignee: Arxon Spiel & Freizeit GmbH
Priority date: 1981-03-19
Filing date: 1982-03-18
Publication date: 1983-01-19
Also published as: FR2502021A1; DE3110834A1

Abstract

A dodecahedron is divided by planes extending parallel to its pentagonal faces, giving 20 corner pieces (E), 30 edge pieces (K), 12 surface pieces (F), and a core piece (not shown) which is a smaller solid dodecahedron. Each surface piece (F) defines a canopy under which lugs and projections, of corner and edge pieces, locate. Each surface piece is rotatably mounted by a headed peg being received in a respective hole of the inner dodecahedron. <IMAGE>

Description

SPECIFICATION Dodecahedrnn toy The invention relates to a dodecahedron (a regular 12-sided figure) consisting of 63 individual parts which can be displaced relative to one another in the manner of a sliding puzzle. It is suitable for children and adults as an educational solitaire game which develops in an amusing way logical thinking, concentration, perseverance and the ability to imagine three-dimensional relationships. These aptitudes are of increasing importance in the highly technological world of today. Furthermore, the dodecahedron solitaire game can be used in the teaching of mathematics to illustrate a large number of basic concepts and results of group theory and geometry.

Among known articles, the so-called Rubik Cube (magic cube, Rubik's Cube) comes nearest to the dodecahedron solitaire game and is described in Hungarian Patent No.170,062 of 30.1.1975.

However, as a relatively unknown platonic solid in which there are no right angles, the dodecahedron is much more suitable for teaching the ability to imagine geometric relationships in space than a cube which is one of the simplest geometrical figures. Whereas, in the Rubik Cube, only 8 corner pieces, 12 edge pieces and 6 surface pieces are movable, 6 colours being mixed when the sides of the cube are given different colours, in the dodecahedron solitaire game this is the case with 20 corner pieces congruent to one another, 30 edge pieces congruent to one another and 1 2 surface pieces congruent to one another, and when the 12 sides of the dodecahedron are given different colours these 12 colours are mixed.

Technical Solution; A dodecahedron is limited by 1 2 regular pentagonal sides. When the dodecahedron is cut with 12 planes, each of which extends parallel to one side of the dodecahedron at a distance d which is the same for all the planes, then the dodecahedron breaks down into 20 corner pieces E, 30 edge pieces K, 12 surface pieces F and a central piece Z (a smaller dodecahedron), see Fig. 1. (On the one hand, the distance d must be sufficiently small so that two planes belonging to sides of the dodecahedron which are not adjacent to one another do not intersect within the dodecahedron.

On the other hand, it must be sufficiently large so that the technical solution described below is possible.) By means of recesses and appendages for these 63 individual parts, which are described exactly in the following exemplary embodiment, it is possible to ensure that each of the 12 layers, which are assigned to the individual sides of the dodecahedron and which each consist of a surface piece F (see Fig. 1 0), 5 edge pieces K (see Figs. 6 and 8) and 5 corner pieces E (see Figs. 7 and 9), can be rotated arbitrarily about its centre axis relative to the remaining dodecahedron body (see Fig. 2). Each corner piece E is always located in 3 of these layers and each edge piece K is aiways located in 2 of these layers, and successive rotations of various layers through integral multiples of 72 allow each corner piece E to be transported from each of the 20 corners to every other corner (with 3 possible positions at this corner) and each edge piece K to be transported from each of the 30 edges to every other edge (with 2 possible positions on this edge).

The appendages and recesses mentioned are to be designed so that 1. the layers can be rotated as desired, 2. the dodecahedron does not fall apart in any phase of movement, and 3. the dodecahedron can be assembled easily from the individual components. There are various possibilities for this. The following process of geometrical construction described as an exemplary embodiment leads to a relatively simple solution.

Exemplary Embodiment; The already cut-up dodecahedron (Fig. 1) may be thought of as being cut with 12 further planes, each of which extends parallel to one side of the dodecahedron at a distance d' which is a little greater than the distance d between the old sectional planes, see Fig. 3. Each of the layers of thickness d'-d which are obtained in this way may be thought of as being cut further with a circular cylinder according to Fig. 4 perpendicular to the sectional planes. It then breaks down into 71 individual parts (of which 10 parts congruent to the parts designated by 0 are not visible in the drawing). The parts are designated in Fig. 4 by F, K or E, depending on whether they are to be connected to an adjacent surface piece F, an adjacent edge piece K or an adjacent corner piece E (appendages).The 20 small parts designated by 0 are omitted completely.

The surface pieces F are to be fastened rotatively and slightly resiliently to the central piece Z. There are various possibilities for this also, and a push button solution seems to be the simplest, as indicated in Figs. 10 and 11. The assembly of all the parts, with the exception of the 11 parts (1 surface piece F, 5 edge pieces K and 5 corner pieces E) belonging to a complete disc, presents no problem at all. Even the last disc can be assembled without difficulty at the end, since the cylinder considered above in the description of the geometrical construction of the recesses and appendages, is perpendicular to the sectional planes.

1. Dodecahedron toy, characterised in that a dodecahedron consists of individual building blocks, and (a) one building block (surface piece) is assigned to each of the 12 sides of the dodecahedron, one building block (edge piece) is assigned to each of the 30 edges of the dodecahedron, and one building block (corner piece) is assigned to each of the 20 corners of the dodecahedron, and (b) for each of the 12 sides of the dodecahedron, the building-block layer, which consists of the surface piece assigned to this side and of the adjoining edge and corner pieces, can be rotated arbitrarily about its axis of symmetry,

**WARNING** end of DESC field may overlap start of CLMS **.

Claims

**WARNING** start of CLMS field may overlap end of DESC **.

SPECIFICATION Dodecahedrnn toy The invention relates to a dodecahedron (a regular 12-sided figure) consisting of 63 individual parts which can be displaced relative to one another in the manner of a sliding puzzle. It is suitable for children and adults as an educational solitaire game which develops in an amusing way logical thinking, concentration, perseverance and the ability to imagine three-dimensional relationships. These aptitudes are of increasing importance in the highly technological world of today. Furthermore, the dodecahedron solitaire game can be used in the teaching of mathematics to illustrate a large number of basic concepts and results of group theory and geometry.

Among known articles, the so-called Rubik Cube (magic cube, Rubik's Cube) comes nearest to the dodecahedron solitaire game and is described in Hungarian Patent No.170,062 of 30.1.1975.

However, as a relatively unknown platonic solid in which there are no right angles, the dodecahedron is much more suitable for teaching the ability to imagine geometric relationships in space than a cube which is one of the simplest geometrical figures. Whereas, in the Rubik Cube, only 8 corner pieces, 12 edge pieces and 6 surface pieces are movable, 6 colours being mixed when the sides of the cube are given different colours, in the dodecahedron solitaire game this is the case with 20 corner pieces congruent to one another, 30 edge pieces congruent to one another and 1 2 surface pieces congruent to one another, and when the 12 sides of the dodecahedron are given different colours these 12 colours are mixed.

Technical Solution; A dodecahedron is limited by 1 2 regular pentagonal sides. When the dodecahedron is cut with 12 planes, each of which extends parallel to one side of the dodecahedron at a distance d which is the same for all the planes, then the dodecahedron breaks down into 20 corner pieces E, 30 edge pieces K, 12 surface pieces F and a central piece Z (a smaller dodecahedron), see Fig. 1. (On the one hand, the distance d must be sufficiently small so that two planes belonging to sides of the dodecahedron which are not adjacent to one another do not intersect within the dodecahedron.

On the other hand, it must be sufficiently large so that the technical solution described below is possible.) By means of recesses and appendages for these 63 individual parts, which are described exactly in the following exemplary embodiment, it is possible to ensure that each of the 12 layers, which are assigned to the individual sides of the dodecahedron and which each consist of a surface piece F (see Fig. 1 0), 5 edge pieces K (see Figs. 6 and 8) and 5 corner pieces E (see Figs. 7 and 9), can be rotated arbitrarily about its centre axis relative to the remaining dodecahedron body (see Fig.

2). Each corner piece E is always located in 3 of these layers and each edge piece K is aiways located in 2 of these layers, and successive rotations of various layers through integral multiples of 72 allow each corner piece E to be transported from each of the 20 corners to every other corner (with 3 possible positions at this corner) and each edge piece K to be transported from each of the 30 edges to every other edge (with 2 possible positions on this edge).

The appendages and recesses mentioned are to be designed so that 1. the layers can be rotated as desired, 2. the dodecahedron does not fall apart in any phase of movement, and 3. the dodecahedron can be assembled easily from the individual components. There are various possibilities for this. The following process of geometrical construction described as an exemplary embodiment leads to a relatively simple solution.

Exemplary Embodiment; The already cut-up dodecahedron (Fig. 1) may be thought of as being cut with 12 further planes, each of which extends parallel to one side of the dodecahedron at a distance d' which is a little greater than the distance d between the old sectional planes, see Fig. 3. Each of the layers of thickness d'-d which are obtained in this way may be thought of as being cut further with a circular cylinder according to Fig. 4 perpendicular to the sectional planes. It then breaks down into 71 individual parts (of which 10 parts congruent to the parts designated by 0 are not visible in the drawing). The parts are designated in Fig. 4 by F, K or E, depending on whether they are to be connected to an adjacent surface piece F, an adjacent edge piece K or an adjacent corner piece E (appendages).The 20 small parts designated by 0 are omitted completely.

The surface pieces F are to be fastened rotatively and slightly resiliently to the central piece Z. There are various possibilities for this also, and a push button solution seems to be the simplest, as indicated in Figs. 10 and 11. The assembly of all the parts, with the exception of the 11 parts (1 surface piece F, 5 edge pieces K and 5 corner pieces E) belonging to a complete disc, presents no problem at all. Even the last disc can be assembled without difficulty at the end, since the cylinder considered above in the description of the geometrical construction of the recesses and appendages, is perpendicular to the sectional planes.

1. Dodecahedron toy, characterised in that a dodecahedron consists of individual building blocks, and (a) one building block (surface piece) is assigned to each of the 12 sides of the dodecahedron, one building block (edge piece) is assigned to each of the 30 edges of the dodecahedron, and one building block (corner piece) is assigned to each of the 20 corners of the dodecahedron, and (b) for each of the 12 sides of the dodecahedron, the building-block layer, which consists of the surface piece assigned to this side and of the adjoining edge and corner pieces, can be rotated arbitrarily about its axis of symmetry, and an arbitrary sequence of these layers can be rotated through integral multiples of 72 , as a result of which the edge pieces change places with one another and the corner pieces change places with one another.