http://mathworld.wolfram.com/RollingPolyhedronGraph.html https://math.stackexchange.com/users/11955/ed-pegg If you roll the tetra-tetra on the plane, toppling it over edges, there are only 12 orientations while rolling. I On Tuesday, December 17, 2019, 07:26:22 PM CST, Fred Lunnon <fred.lunnon@gmail.com> wrote: Not sure that I've understood this --- is it a statement about the symmetry group of some isohedral tiling of the plane? WFL On 12/18/19, ed pegg <ed@mathpuzzle.com> wrote:
Let t^2 =1.92756 be the tetranacci constant. Build a tetrahedron with edgelengths t^0 opposite t^3 t^1 opposite t^1 t^2 opposite t^2
This has 4 similar triangles of 2 sizes.
If this tetrahedron is rolled on its edges, it only reaches 12 different orientations. -Ed Pegg Jr
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