Re: A dekany graph with 3-fold symmetry

Sorry, mistake in my descr. of truncated simplex.

Tetrahedron truncated to midpoint of edges = octahedron of course
(you can make a tetrahedron by adding smaller tetrahedra to
four non adjacent faces of octahedron).

For picture of octahedron as truncated tetrahedron, see my pic at
http://www.rcwalker.freeserve.co.uk/cubeetc/index.htm
(3rd pic on page with red tetrahedron and black octahedron)

So the octahedra are the truncations of the tetrahedral faces of the original simplex.

The tetrahedra are the new 3-D faces that appear at the vertices on truncation,
and their triangular faces are obtained by joining mid points of lines that meet
at the vertex.

4 lines meet at each vertex of simplex, so as there are 4 ways
of choosing 3 out of 4, that makes the 4 faces of the tetrahedron.

Robert