software3d.com Forum Index software3d.com
Software3D Forums
 
 FAQFAQ   SearchSearch   MemberlistMemberlist   UsergroupsUsergroups   RegisterRegister 
 ProfileProfile   Log in to check your private messagesLog in to check your private messages   Log inLog in 

Polyhedral Chess Set

 
Post new topic   Reply to topic    software3d.com Forum Index -> Polyhedra
View previous topic :: View next topic  
Author Message
Nordehylop



Joined: 27 Feb 2008
Posts: 21
Location: Illinois, USA

PostPosted: Sun May 04, 2008 7:31 pm    Post subject: Polyhedral Chess Set Reply with quote

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.
_________________
It's always darkest just before it goes pitch black.
Back to top
View user's profile Send private message Visit poster's website
Jabe



Joined: 12 Jan 2008
Posts: 46
Location: Somewhere between Texas and the Fourth Dimension

PostPosted: Mon May 05, 2008 6:25 am    Post subject: Reply with quote

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"
_________________
May the Fourth (dimension) be with you.
Back to top
View user's profile Send private message Visit poster's website
Nordehylop



Joined: 27 Feb 2008
Posts: 21
Location: Illinois, USA

PostPosted: Wed May 07, 2008 9:38 pm    Post subject: Reply with quote

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.
_________________
It's always darkest just before it goes pitch black.
Back to top
View user's profile Send private message Visit poster's website
robertw
Site Admin


Joined: 10 Jan 2008
Posts: 395
Location: Melbourne, Australia

PostPosted: Thu May 08, 2008 5:46 am    Post subject: Reply with quote

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



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.
Back to top
View user's profile Send private message Visit poster's website
Display posts from previous:   
Post new topic   Reply to topic    software3d.com Forum Index -> Polyhedra All times are GMT
Page 1 of 1

 
Jump to:  
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum


Powered by phpBB © 2001, 2005 phpBB Group
Protected by Anti-Spam ACP