
10052019, 04:11 PM
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#1
Why do the Catalan solids only have one dihedral angle listed on wikipedia?
Also, can they be slightly altered to roll better (discounting rounding of edges) yet still be face transitive and fair dice?
Basically get all of the dihedral angles as close to the same will still having all faces the same
As an example this is a picture of the d48 which is a disdyakis (rhombic) dodecahedron
https://en.wikipedia.org/wiki/Disdyakis_dodecahedron
Face "1" has edges A, B and C (short to long) with A adjacent to 34, B next to 42 and C alongside of 8.
So there are three different dihedral angles a, b and c (or alpha, beta and gamma if you like).
Basically, I want to get all of the dihedral angles as close to the same will still having all faces the same.
In the picture below all of the "A" type edges (1/34, 8/47, 33/10 etc) will remain in place while the B and C edges (1/8, 8/33, 33/45) get shorter because the pinwheel square pyramid height they rise from is getting shorter.
Last edited by repoman; 10052019 at 04:27 PM.

10062019, 09:11 PM
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#2
They only have one dihedral angle (by duality, since Archimedean solids have a single edge length). Did you mean a different kind of angle?

10072019, 01:43 AM
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#3
Guess I have lying eyeballs, because I did the math (dusted off an old textbook for angles between planes) for the tetrakis hexahedron and I that that angles between both types of edges are 143 degrees, 7'48"
https://en.wikipedia.org/wiki/Tetrakis_hexahedron
This says more about my pyschology of visual spatial center than anything else.
Edited to add that I took out my calipers on the die and I found that instead of the tetrakis pyramids being a/4 above the cube base they were only about a/8 above that.
Huh, so it is A tetraxis hexahedron it is not THE standard one that is the dual of the truncated octahedron.
Well they sell lotsr of cool dice at any rate.
https://www.mathartfun.com/d141518.html
Last edited by repoman; 10072019 at 02:40 AM.
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