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THE PUZZLE SQUARES

One type of square with integral ball and socket hinges does it all! Each edge has either 2 ball hinges or 4 socket hinges. These are spaced so you can hinge 2, 3 or 4 squares together, edge to edge, in 9 different combinations.

 

Puzzle squares are injection molded plastic panels with open centers. They come in two colors.

The blue and green puzzle square panels are translucent. Frosted white is available via special order.

2,3, or 4 squares can be hinged together in 9 combinations as follows: A+A-, B+B-, A+B-, B+A-, B+B-A+, A+A-B+, B+B-A-, A+A-B-, A+A-B+B-,

The kit includes a 6-page colored booklet with 24 illustrated constructions which indicate the number of squares needed to build each.

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TOWERS, WHEELS AND BASICS

Below are a few basic assemblies (figure 13). They occur in many of the more complex constructs. The Ferris wheel (right) combines cubes and prisms.

Some of the simpler constructions from the booklet (plus towers, chains, and triangles) are shown below. (Figure 15)
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Each set contains 48 squares (50% green & 50% blue), the booklet, and 24 straws of various lengths and diameters. The box is made of heavy corrugated paper and is suitable for storage.

13.

 

TRANSFORMING 3D LATTICES FROM
2D TESSELLATIONS AND ROTATORS

A HEX/ Diamond transforming lattice (Figure 17)

Figure 19 is one transformed version of figure 17.
Two rotators, one with 8 type 'D' assemblies, (figure 20), with complete rotation, and one with 6 cubes with partial rotation (figure 21).
8 type 'B' constructs link together forming 2 half octas.

GLOBES, LANTERNS, AND FOOTBALLS FROM FERRIS WHEELS
Four of the Ferris wheel's basic 'A' units and two 'B' cubes (figure 23), create a globe (figure 25); below
Elongating 4 basic 'A' Ferris wheel units plus 2 'B' cubes produces the lantern (figure 26). Using 3'A' units with two triangular prisms for the 'B' units produces the football (figure 27).
Two layers of edge-hinged cubes stacked corners to corners (figure 29).
Big cube with interior and exterior squares all inter-hinged, thirty-six squares. (Figure 33) eight straws join at the cube's center.

THINGS, PUMPS, AND MORE CUBES
Some fun building types with added landscape in one (the bridge left), and the other with airplane, pilot, and tank (figure35). Below
Three types of pumps. The three way, from drawing (15) in the booklet, the four way, not pictured here, and the six way (figures 37, 38).
Double observation spheres. A combo of cube bases and the small balls from booklet drawing #23. (Figure 39)
(Figure 41) is a transformer. It is a multi-directional one but very simple. It requires four type 'C' prisms and 16 squares forming 4 open ended prisms.
There are several polyhedra which can be extroverted from a virtual polyhedron. In drawing (45) below a virtual tetra is extroverted with four type 'B' prisms.

For serious puzzle builders, explorers, and geometry buffs

(Figure 43) is an extroverted tetra-dipyramid. surfaced with 12 squares.

 

Below (figure 47) is an extroverted cubocta.

4 type 'B' constructs link together creating one central negative tetra, extroverting step one.

Some extroverted polyhedra transform. The simplest are the rhomba (figure 53)and the rhombic dodeca (figure 45). The former has six diamond faces.

The rhombic dodeca shown below has 12 diamond faces.

The ridged extroverted cubocta (figure 47) has six cubes and eight triangular prisms; Its exterior face is comprised of 30 squares.

Chain of type 'B' constructs link together forming a twisting chain.

Extroverted transforming polyhedra, as with the simplest rhomba, are those with square, pent or hex open-ended prisms #49, #51, #53, #57.

 

The Rhombic dodeca (figure 49) can be made rigid with the addition of 30 face squares. The extroverted truncated octa (figure 51) requires eight hex and six square prisms, all open ended.
The rhomba (figure 53 is shown extroverted & in collapsed form) has 6 diamond faces. Sixteen squares are added to the exterior. These transform into square prism Sketch 55 below shows the basic extroversion of six square prisms around a virtual cube.

The extroverted pentagonal dodeca has twelve pentagonal prisms. It is also a transformer (figure 57).

See also (figure 72) below, where this figure has been made rigid.
The big helix is comprised of two basic prism types 'B' and 'C'. 'B' is for turning and 'C' is for climbing. (Figure 59) below.
The building complex, (61) below, is derived by transforming and increasing the height of selected parts of lattice (figure 17). Paper cutouts, model people, and cars complete the complex.
Roger Penrose's tiling can be treated as a transforming lattice. Here is a drawing showing just one portion of it (figure 63) below.
Top view of bldg complex #61.

Now you are ready to exercise all of your creative juices using your new-found skills to create models of your own design.

Top view of Penrose tile, complex tesselation

Straws are used to reiterate basic designs, add color, and discover hidden interior polyhedra. Various sized straws fit between hinged squares and are held there by friction.

(70) is a extroverted rhombic dodeca (figure 49) made rigid with the addition of 30 face squares. Resultant face also has 8 triangles and 12 diamonds. (Note inscribed cube and octa.

(72) is an extroverted pentagonal dodeca (as in 57) made rigid with 60 face squares. The resultant face also has 12 pents, and 30 triangles. It is called a Rhombicosidodeca.
 

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