Talk:Snub icosidodecadodecahedron

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[edit] Cartesian coordinates of snub icosidodecadodecahedron

NOTE: Message below posted from email I received.

First, thank you for your work on polyhedra. I am myself trying to recompute all exact data and particularly coordinates of all interesting polyhedra. For validation of my results, I use wikipedia which is the only place where I was able to found exact coordinates.

All given coordinates are correct, except for U46. The vertex figure is 3.3.3.5.3.5/3. So at each vertex, they are six concurrent faces and then six concurrent edges having the same length. But with the given data it is totally impossible to find them. In fact it was also impossible to find three edges of same length concurrent to any vertex, and a fortiori to generate a uniform polyhedron, so something was wrong (it was not a thought, but a fact).

As the information you give for other polyhedra is totally correct, it was obvious they was just a small typing error. I don't thought it was an error in the vertex formula, as they have the same norm (except maybe a sign error). So, I had high doubts for α, β and γ formula.

To find the error I made a numerical analysis on the distortion of the vertice cloud by applying variations on β and γ.

I find that for values β=9.6805 and γ=3.8983 - with a very high probability - provide the vertice of the snub icosidodecadodecahedron.

But these values are your values, but with β, γ inverted.

So I inverted them and the topological analysis directly provided me all the correct faces of the snub icosidodecadodecahedron (all radii, lengthes, angles correct at 40 decimals).

Sorry if this was done using numerical methods but I was to lazy to try to recompute vertice using symbolic algebra.

I have made this for snub cube and snub dodecahedron using three different methods

• Direct computation using face translation and rotation
• Multitruncation and alternation
• Resolution using Schwarz triangles and spherical trigonometry.

I took me many days, so I didn't try (yet) to redo this for the snub uniforms...

Thanks for your formula... and sorry for my poor english.

Alain Lassine

Hi Alain. I appreciate your efforts. I don't have time to confirm your work now. I'll see if I can track who added them originally from the history. Tom Ruen 21:00, 8 June 2007 (UTC)

I left a message at User_talk:Robert_Stanforth, and restored your changes for now. I hope Robert is active and is able to help confirm your changes. Tom Ruen 21:11, 8 June 2007 (UTC)

I have reviewed this change, and confirm that the fix is correct: I had erroneously reversed the values for beta and gamma. Thank you very much for your efforts in verifying my expressions! Robert Stanforth 16:05, 14 October 2007 (UTC)