non-tetrahedrizable polyhedron

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dysphras
Posts: 5
Joined: Tue Jun 10, 2008 8:40 am

non-tetrahedrizable polyhedron

Post by dysphras » Wed Jun 11, 2008 10:52 am

Hi everybody,

Here are the coordinates for the celebrated *Schonhardt's non- tetrahedrizable polyhedron*. Please copy the following in *txt* format, save with the extension *off* and open it with Stella. It's dead simple.
Enjoy! 8)

Schonhardt's polyhedron:

6 8 12
0.0 1.0 0.82644582514053474004
0.86602540378443864676 -0.5 0.82644582514053474004
-0.86602540378443864676 -0.5 0.82644582514053474004
-1.0 0.0 -0.82644582514053474004
0.5 0.86602540378443864676 -0.82644582514053474004
0.5 -0.86602540378443864676 -0.82644582514053474004
3 0 1 5
3 0 5 4
3 0 4 2
3 0 2 1
3 3 1 2
3 3 2 4
3 3 4 5
3 3 5 1

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robertw
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Post by robertw » Wed Jun 11, 2008 12:19 pm

Cool, I didn't know there was such a thing. I believe it always works in 2D, that any non self-intersecting polygon can be divided into triangles just using the original vertices. I hadn't realised that the equivalent wasn't always possible in 3D.

Rob.

dysphras
Posts: 5
Joined: Tue Jun 10, 2008 8:40 am

Post by dysphras » Thu Jun 12, 2008 8:29 am

Cool, I didn't know there was such a thing. I believe it always works in 2D, that any non self-intersecting polygon can be divided into triangles just using the original vertices. I hadn't realised that the equivalent wasn't always possible in 3D.
Glad you liked it. I will try to post here hopefully nontrivial stuff about polyhedra & polychora as time permits.

Best,
Claudio

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