Polyhedral Chess Set

For general discussion of polyhedra, not necessarily Stella-specific.
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Nordehylop
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Polyhedral Chess Set

Post by Nordehylop » Sun May 04, 2008 7:31 pm

I had the idea a while ago of building a chess set with the regular polyhedra as the pieces. Only one problem: six chess piece types, five regular polyhedra. Unsurprisingly, the knight was the odd one out, but here is what I came up with for the other five (and some of the reasoning behind the choices):

Pawn: Tetrahedron. Simplest polyhedron paired with the least valuable chess piece

Rook: Cube. both feature right angles in their movement/shape

Bishop: Octahedron. The dual of the cube is the octahedron, and you could say that the dual of the rook is the bishop (rook moves orthogonally, bishop diagonally).

King: Dodecahedron. The dodecahedron is the most impressive looking regular polyhedron, and so it should be paired with the king, the most important chess piece.

Queen: Icosahedron. The icosahedron and dodecahedron go together, the king and queen go together.

If anyone has any suggestions for the knight, I would be grateful.
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Jabe
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Post by Jabe » Mon May 05, 2008 6:25 am

The cuboctahedron might be a good choice, its vertex figure is a rectangle which consists of two L's - the L move is a nights move. Oh by the way, hope ya'll had a good May 4th, and "May the Fourth be with you"
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Nordehylop
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Post by Nordehylop » Wed May 07, 2008 9:38 pm

Another advantage of the cuboctahedron is that its move could be thought of as a cross between the bishop's diagonal and the the rook's othogonal move. Another idea that I had was to use the snub disphenoid (J84) because it is isohedral like the other pieces but has a sort of twisted look. My dad wants me to use the Szilassi polyhedron (which looks very knight-like), but it would look very complex compared to the others.

Any ideas for the materials for this chess set? Paper would probably be too light, and I don't have all of the tools for making wood pieces.
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robertw
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Post by robertw » Thu May 08, 2008 5:46 am

Good idea. Did you notice this picture from my site?

Image

It's from this page: http://www.software3d.com/KingStella.php

Pity we're not in 4D, as there are 6 convex regulars there! And they'd match the pieces quite well.

In 3D, it's not very intuitive to me which roles the dodecahedron and icosahedron should have. I could equally well see the icosahedron as the king and the dodecahedron as the queen.

The snub cube might work well as the knight, since it is chiral which seems to match the way it moves, but I agree it's probably better to go with the cuboctahedron, a shape which would better match the simplicity of the other pieces. Also, it sits between the cube and the octahedron, another reason to go with the cuboctahedron.

If possible, it would be nice if the octahedron could sit on a point. I guess it would need a small stand attached to one vertex.

It would be nice to see some nonconvex shapes too, like the stella octangula, but maybe as a separate project.

Materials: I only know how to make stuff out of paper, so that would be my choice. But it would be great to see the pieces made from glass or crystal otherwise!

Rob.

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