Octahedron

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Description :

A twisted octahedron.
The stuts come in four sets of three parallel struts which
run along the middle of equilateral triangle channels. These
correspond to the positions of a particular
packing of rods with a triangular cross section.
This helps make the twisted octahedron a popular base for
wooden puzzles
Example puzzles





Octahedron / Cube

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Description :

The midpoint of twisting between an octahedron and cube.
The cords form a cuboctahedron, having the six faces of the
cube and 8 faces of the octahedron. The struts form four
triangles inscribed in the equatorial hexagons of the
cuboctahedron.
Example puzzle





Cube

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Description :

A twisted cube.
Example puzzle





Cuboctahedron

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Description :

A twisted cuboctahedron.





Cuboctahedron / Rhombic Dodecahedron

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Description :

The midpoint of twisting between a cuboctahedron and rhombic dodecahedron.
The cords form a shape close to a small rhombicuboctahedron. It has the
14 faces of the cuboctahedron (6 squares and 8 triangles) and the 12
rhombi of the rhombic dodecahedron. The struts are arranged as 6 squares,
arranged in parallel pairs offset by an 1/8 of a turn.





Rhombic Dodecahedron

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Description :

A twisted rhombic dodecahedron (viewed along a twofold axis).
Example puzzle





Rhombic Dodecahedron

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Description :

A twisted rhombic dodecahedron (viewed along a fourfold axis).
Example puzzles





Icosahedron

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Description :

A twisted icosahedron. Like the twisted octahedron it has sets of
parellel struts  in this case 5 sets of 6 struts. The triangular
channels these run through are the shape of a golden gnomon, the
triangle made from joining three consequetive points on a pentagon.
This makes it another popular choice for wooden puzzles, as
is described in this discussion of the
Jupiter
Example puzzles





Icosahedron / Dodecahedron

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Description :

The midpoint of twisting between an icosahedron and dodecahedron.
The cords form an icosidodecahedron, having the 12 faces of the
dodecahedron and the 20 faces of the icosahedron. The struts form six
pentagons inscribed in the equatorial decagons of the icosidodecahedron.





Dodecahedron

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Description :

A twisted dodecahedron.





Small Stellated Dodecahedron

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Description :

A twisted small stellated dodecahedron (viewed along a fivefold axis).
Example puzzles





Small Stellated Dodecahedron

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Description :

A twisted small stellated dodecahedron (viewed close to a twofold axis).
Example puzzles





Small Stellated Dodecahedron

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Description :

A twisted small stellated dodecahedron (viewed close to a threefold axis).
One of the features of the twisted polyhedra is that each strut is
paired with a parallel line on the other side of the centre through
which lots of struts (possibly extended) pass. This feature is quite
striking in this view. Three parallel struts are seen endon, each paired
with a line of crossing. Of the other struts, 24 pass through just
one line, and three pass through two. Here is another example showing a
crossing line in a twisted cube
The property is taken good advantage of in this
30 Notched Sticks
puzzle. The configuration of the pale sticks is a mirror image of
that of the hexagonal sticks, with the two being related by a central
inversion.
Example puzzles





Stella Octangula

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Description :

A twisted stella octangula (viewed along a fourfold axis).
The usual connection method was unstable in this polyhedron so
the 8way vertices have been connected slightly differently. If
connected by the usual way the stella octangula would be the
twisted dual of the truncated cube.





Stella Octangula

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Description :

A twisted stella octangula (viewed along a threefold axis).
The usual connection method was unstable in this polyhedron so
the 8way vertices have been connected slightly differently. If
connected by the usual way the stella octangula would be the
twisted dual of the truncated cube.




