All this stuff is to be found in Coxeter's book "Regular Polytopes", or (less technically) in Cundy & Rollet "Mathematical Models". There are 5 ways to inscribe the 8 vertices of a cube among the 20 vertices of a dodecahedron; and dually, 5 ways to circumscribe the 8 faces of an octahedron around the 20 faces of an icosahedron. Googling "regular compound polyhedron" turns up among others http://en.wikipedia.org/wiki/Polyhedral_compound http://www.georgehart.com/virtual-polyhedra/compounds-info.html Fred Lunnon On 9/12/09, mcintosh@servidor.unam.mx <mcintosh@servidor.unam.mx> wrote:
Quoting rcs@xmission.com:
Is there something similar connecting the regular icosahedron and the regular octahedron? It will have to be a little different, since 6|12 but 8~|20.
They are face duals. This may carry over to embedment.
-hvm
------------------------------------------------- www.correo.unam.mx UNAMonos Comunicándonos
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun