non-tetrahedrizable polyhedron

[dysphras]

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!

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

[robertw]

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]

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