GB2113104A - 4 x 4 x 4 movable block puzzle - Google Patents

Abstract

The puzzle comprises a plurality of members captive to but movable in 4 x 4 sets about any of three mutually perpendicular rotational axes relative to a core. Twelve inner blocks (10), positioned between pairs of arms (2), and six arms (2) serve to retain and guide external blocks (20,30 and 40). Numerous regular and non-regular solids are contemplated as the external shape of the puzzle, <IMAGE>

Description

SPECIFICATION A mechanism for modelling groups This invention relates to a mechanism for modelling groups.

The mechanism is primarily intended for use in devices that demonstrate combinations and permutations, and in devices that physically model some of the mathematics involved in the theory of groups. Devices embodying the mechanism may be brightly coloured and may also have some amusement value.

According to the present invention there is provided a mechanism for modelling groups comprising a piurality of members captive to but movable in sets in any of three discrete rotational modes relative to a base structure, the choice of set determining the axis of rotation, the members presenting six groups of elements in a start position each of which have a characteristic or feature identifiable with a particular group, and the movement in sets re-distributing the elements to form variant groups, wherein each group comprises 16 elements in a 4 x 4 array.

Generally, the starting groups will all be different, although it is possible in a simplified version to have two or more the same, or matched pairs for example.

In the preferred form, there are 56 members forming a cube, each member having a block-like portion presenting one, two or three exposed square faces, totalling 96, on which said elements are provided. There can be variations on this, for example the sides may be made concave or convex, even to the extent of developing it into a sphere or cylinder. Further variations of the outer shape can be achieved by trimming down four parallel edges with a chamfer, to form a barrel with polygonal cross section, or by chamfering all twelve edges to form a diamond shape.

Alternatively, the eight corners can be trimmed to form a polyhedronal cube.

The elements of each starting group may simply be distinguished by colour and/or pattern.

The colours may be plain, so that each side of the cube in the starting position is completely red, blue, green and so on. However, alternatives may be adopted, such as using flags as the elements, or simply patterns in monochrome. In other versions, the elements may be distinguished by projections or depressions relative to the base surface. For example, the elements may be represented by the numbers 1 to 6 in "dot" form as on dice, with studs or dimples on the exposed faces arranged accordingly. In another variation, there may be projections of different lengths or shapes.

The base structure will generally be a six-armed spider, with arms co-incident with the rotational axes mutually at right angles or aligned in opposite directions from a central boss.

Reference will hereafter be made exclusively to what we regard as the standard form, with blocks arranged to form a cube, and with each face of the cube consisting of a total of 1 6 faces, one from each of 1 6 blocks. The blocks that lie at the corner of the cube have three visible faces, the blocks that lie along the edge of the cube have two visible faces, and the rest of the blocks have one visible face. Concealed within the cube is a logical mechanism that enables the blocks to be moved in relation to each other into a vast number of different combinations, yet at all times ensuring that all of the blocks are securely attached to each other.

The mechanism will allow any face layer of 16 blocks to be rotated about the axis perpendicular to that face through its centre. The mechanism will also allow any of the inner layers of 12 blocks, presenting 1 6 visible faces, to be rotated about the central axis perpendicular to that layer. Thus each individual block lies in three different planes of rotation, that is it forms part of three separate layers of blocks, each layer being at right angles to the other two.

By rotating different layers of blocks in different orders it is possible to move the blocks in almost any imaginable combination. There are some limitations: the blocks constituting the corners of the cube always move to a corner position, the blocks at the edges of the cube always move to an edge position, and blocks with only one face showing remain confined adjacent the centres of the cube faces.

There are basically three different types of exposed block: corner block, edge block and face block, but in the preferred form there are also concealed inner blocks forming part of the logical mechanism. These types are described more fully later.

An example of some of the combinations that can be realised with this mechanism is that it is possible to move any individual corner block to any other corner position and have it in any of the three possible orientations. It is then possible to move any one of the 7 remaining corner blocks to any of the 7 remaining corner positions, in any orientation, followed by any one of the 6 remaining corner blocks to any one of the 6 remaining corner positions, in any orientation and so on until the last corner where there is obviously no choice as to which position it can go in, and there is no choice of its orientation.

In addition to the above permutations it is possible to have at the same time any combination of permutations of the edge blocks and of the face blocks.

Continuing the above example, we have the choice for every one of the corner block combinations, of being able to move any one of the 24 edge blocks to any one of the 24 edge positions and then have any one of the remaining 23 edge blocks moved to any one of the remaining 23 edge postions and so on until the last 2 edge blocks remain and there is no choice once one of them is positioned as to which position the final one can go in. The process can be repeated with the face blocks, the permutations availabie using any one type of block being independent of the permutations available on any other type of block.

The sequence of moves necessary to achieve some of the permutations can be long and of much mathematical interest.

For a better understanding of the invention, the standard constructional form will now be described, by way of example, with reference to the accompanying drawings, in which: Figure 1 is an isometric view of a logic device, with some parts removed and others in ghost, Figure 2 is a view of a central logical mechanism on the line Il-Il of Figure 1, Figure 3 is a view of an inner layer or array of blocks on the line Ill-Ill of Figure 1, Figure 4 is a view of an outer layer or array of blocks on the line IV-lV of Figure 1, Figure 5 is three isometrics showing three axial rotation of some outer layer arrays, Figure 6 is three isometrics showing three axial rotation of some inner layer arrays, Figure 7 is two isometric views of a concealed inner block, Figure 8 is two isometric views of a corner block, Figure 9 is two isometric views of an edge block, and Figure 10 is two isometric views of a face block.

The device is in the form of a cube whose faces are formed by blocks in 4 x 4 arrays, the edge and corner blocks being common to two or three arrays. In a start position each face of the cube will be individually and uniformly coloured, or otherwise distinguished from the other faces. The blocks have an interlocking engagement to be described below so that they are all captive to a central six armed spider 1. The interlocking arrangement allows any layer of blocks to be rotated about the axis perpendicular and central to that layer relative to the other blocks of the cube, examples of this being shown in Figures 5 and 6.

The six arms 2 of the spider 1 are cylindrical and their axes correspond to the X, Y and Z axes of a three dimensional orthogonal system. These will be referred to as the main cube axes. At the end of each arm 2 there is mounted a 'mushroom' head 3, square when viewed end-on to the arm, with arcuate side faces 4 and a central square stem 5 that normally abuts the end of the arm. The convex outer face 6 and concave inner face 7 of the head 3 each have double cylindrical curvature, the centres being the axes of the arms 2 mutually at right angles to the arm in question. The head 3 is held in position by a screw 8 whose head is recessed into the face 6, but between the screw head and the base of the recess there is a coil spring 9 so that the head 3 can be moved away slightly from the centre of the cube. This is necessary for ease of operation.The head 3 can also be rotated about its associated axis, with all the other blocks of its associated face layer behind which it is concealed.

Forming part of the concealed mechanism retaining and guiding the external blocks are twelve inner blocks 10 positioned between adjacent pairs of arms 2, as best seen in Figs. 1, 2 and 7. Each block 10 has a slightly flattened, almost cubic portion 11 with two flat sides 12 tangential to respective arms 2 along their whole length and of a depth corresponding to the thickness of the stems 5. The opposite sides 13 are convex, each with a cylindrical curvature centred on the opposite arm axis, and they terminate at the corner remote from the cube centre in a divergent projection 14. This has an inner cylindrical sector-shaped portion 1 5 of a thickness equal to that of the portion 11 and an outer curved head 16, of comparable size to the heads 4, with inner and outer surfaces centred on the cube axis at right angles to the arms embracing the block 10.Each head 1 6 is spaced from adjacent heads 4, but they have the same inner and outer radii of curvature so that almost continuous rings are formed. The spacing is such that any head 4 can rotate with its associated face layer of blocks, without impinging on adjacent heads 16, and such that any head 1 6 can move with an inner layer of blocks without being interfered with by the heads 4.

In addition to these inner blocks there are three other types of block. There are eight corner blocks 20 (Fig. 8), each having three exposed faces 21.

Adjacent them, along the cube edges, there are twenty-four edge blocks 30 (Fig. 9), each of which have two exposed faces 31. To complete the cube there are twenty-four face blocks 40 (Fig. 10), again each with a single exposed face 41. These different block types will be described in turn.

The corner blocks 20 are themselves almost complete cubes. However, at the concealed inside corner there is a substantially hexahedronal lug 22 with symmetry about the diagonal axis. This lug has three faces 23 parallel to the faces 21 which meet and point towards the centre of the cube.

Each of the other three faces 24 is an undercut step from a curved edge 25 centred on the cube axial normal to the associated face 23. It is by means of this lug that each corner block is held captive while still being enabled to turn in any plane with any of the three face layers of other blocks to which it is common.

The edge blocks 30 each have an almost complete square face 32 adjacent a corner block 10, but it is stepped inwardly at the inner corner.

This step 33 has a curvature centred on the main cube axis normal to the plane of the face 32 and accommodates and guides part of the lug 22 of the adjacent corner block (and other formations described below) as it is rotated about that axis.

The opposite face 34 is planar and abuts a mirrorimage edge block.

Each of the other two faces 35, opposite the exposed faces 31, has a curved step 36 centred on the cube axis normal to that face, of a radius equal to that of the edges 25, and of a depth equal to that of the lugs 22. These steps 36 help define a lug 37 of generally right angled triangular form pointing to the centre of the cube, but with an arcuate recess 38 cut into it from the face 34 and centred on the cube axis normal to that face. The innermost portion of the lug 37, to the cube centre side of the recess 38, is of reduced width, having a face 39 set back from the plane of the face 34.

The recess 38 can slidingly accommodate and guide edge portions of the heads 4 and 16, and the hook formation helps to ensure retention of the edge blocks to the assembly.

The exposed face 41 of each face block 40 is not completely square, but has a small cutaway 42 in the corner that will always be at the centre of a cube face. These cutaways combine to form central circular apertures through which access can be gained by an "Allen" key to the screws 8.

The reverse side of this block 40 has a right angled rib 43 bounding on the inside of the angle a centre corner portion which overlies with clearance a quadrant of a head 4. On the outside of the angle the block thickens towards the outer corner, with a double curved surface 44 which matches in reverse and closely co-operates with the steps 36.

At the angle of the rib 43 there is a leg 45 normal to the face 41, terminating in a foot 46 projecting towards the cube axis normal to that face. The mutually facing surfaces of the rib 43 and foot 46 are dimensioned and curved to form smooth continuations of the recesses 38, and the sides 47 of the foot are co-planar with the faces 39.

All but one of these face blocks 40 are free of attachment to the spider. However, one of them is secured to its associated arms 2, for example by adhesive, screws or pins. This ensures that when the assembly is a cube (without any block layer twisted skew to an adjacent layer) the spider is oriented with the arm axes normal and central to the cube faces. Otherwise it would be possible for the spider to swivel out of this position and prevent the operations shown in Figures 5 and 6.

Claims (14)

1. A mechanism for modelling groups comprising a plurality of members captive to but movable in sets in any of three discrete rotational modes relative to a base structure, the choice of set determining the axis of rotation, the members presenting six groups of elements in a start position each of which have a characteristic or feature identifiable with a particular group, and the movement in sets redistributing the elements to form variant groups, wherein each group comprises 16 elements in a 4 x 4 array.

2. A mechanism as claimed in claim 1 in which there are 56 members forming a cube, each member having a block-like portion presenting one, two or three exposed square faces, totalling 96, on which said elements are provided.

3. A mechanism as claimed in claim 2 in which the sides are concave or convex.

4. A mechanism as claimed in claim 2 in which the sides are curved convexly and together form a sphere or cylinder.

5. A mechanism as claimed in claim 2 in which the overall shape is in the form of a barrel with polygonal cross-section or is diamond shaped.

6. A mechanism as claimed in claim 2 in which the eight corners are trimmed to form a polyhedronal cube.

7. A mechanism as claimed in any of claims 1 to 6 in which the elements of each starting group are distinguished by colour and/or pattern.

8. A mechanism as claimed in any of claims 1 to 7 in which the elements are distinguished by projections or depressions relative to the base surface.

9. A mechanism as claimed in any of claims 1 to 8 in which the base structure is a six-armed spider, with arms coincident with the rotational axes mutually at right angles or aligned in opposite directions from a central boss.

10. A mechanism as claimed in any of claims 1 to 9 in which the blocks are arranged to form a cube, each face of which cube consists of a total of 1 6 faces, one from each of 1 6 blocks, the blocks that lie at the corner of the cube having three visible faces, the blocks that lie along the edges of the cube having two visible faces, and the rest of the blocks having one visible face.

11. A mechanism as claimed in claim 10 wherein there is concealed within the cube a logic mechanism that enables the blocks to be moved in relation to each other into a large number of different combinations, yet at all times ensuring that all of the blocks are securely attached to each other.

12. A mechansim as claimed in claim 11 in which the logic mechanism allows any face layer of 1 6 blocks to be rotated about the axis perpendicular to that face through its centre.

1 3. A mechanism as claimed in claim 11 in which the logic mechanism allows any of the inner layers of 1 2 blocks, presenting 1 6 visible faces, to be rotated about the central axis perpendicular to that layer.

14. A mechanism as claimed in claim 1 constructed adapted and arranged to operate substantially as herein described with reference to and as illustrated in the accompanying drawings.