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Topic:  How to calculate the ratio of Platonic solid's duals? 
Related Item:  http://mathforum.org/mathtools/tool/500/ 
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Subject:  ratio of platonic solid's duals 
Author:  Dennis 
Date:  Apr 8 2003 
planar graph is obtained by replacing each face with a vertex. Faces that were
adjacent become vertices connected by a line. this tells us nothing about how
big each graph is.
In the case of the platonic solids you need to decide what the physical
relationship is between a solid and its dual. For example, when you consider
the octahedron as the dual of a cube, do you mean the octahedron inscribed in
the cube with a vertex at the center of each face of the cube, an octahedron
containing the cube with each vertex of the cube at the center of a face of the
octahedron, both inscribed in the same shpere, or some other relationship. Once
you have decided on their physical relationship, their relative volumes can be
calculated.
 
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