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Forum index » Science and Technology » Math » Recreational
Edge Uniform polyhedra?
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Mike Amling
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Joined: 05 May 2005
Posts: 525

PostPosted: Sat Jun 10, 2006 2:05 am    Post subject: Edge Uniform polyhedra? Reply with quote

All of the "regular polyhedra" are edge-uniform as well as being
face-uniform. The two quasi-regular polyhedra (cuboctahedron,
icosododecahedron) are also edge-uniform, as are their duals.
Edge-uniform means that not only are all the edges the same
length, but that they are in identical situations--for any given
pair of edges, there is a rotation that maps the polyhedron onto
itself *and* puts the first edge where the second one used to be.

Are there any other edge-uniform polyhedra besides these nine?
(thirteen if you count the Kepler-Poinsot solids as "regular")

For that matter, if the Kepler-Poinsot solids are counted as
"regular", why isn't the Stella Octangula?



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