
Re: A Theorem concerning the Trisectors of a Triangle
Posted:
Sep 17, 1998 4:37 PM


On Thu, 17 Sep 1998, John Conway wrote: > On Thu, 17 Sep 1998, Russell Towle wrote: > >[...] > > Do we see such behavior in tetrahedra, for instance, with a regular > > Platonic tetrahedron arising from the trisection or quadrisection of a > > solid angle? >[...] > Your question has suddenly produced an interesting thought  maybe > the 3D version involves a Schlegel diagram for the orthoplex > (my preferred name for the crosspolytope) in which the vertex figures > at the vertices of the outer tetrahedron are versions of the Morley figure? > I don't think it can work for a Euclidean tetrahedron, because there > doesn't seem to be a spherical version of Morley; but it could conceivably > work for an ideal tetrahedron in hyperbolic space.
If one trisects the dihedral angles as you suggest, do the opposite endpoints of the rays of vertices of Morley triangles ever/always form the vertices of an ideal regular icosahedron?
Douglas Zare

