Compounding the cube and the octahedron is another way to show that they are


symmetrically identical.  In doing so the vertex of one polyhedron is juxtapositioned


jam201202octacubeaniwhtbkgrnd95x95gif128.gif (6800 bytes)

octacubecomanitrans107x100res100gif255.gif (14325 bytes)

Fig. 7a - Compound cube/

Fig. 7b - 2, 3, and 4-fold


symmetry of cube/octahedron

Required parts

32 large triangles, 6 large squares, 24 right triangles, 72 pinges



Fig. 7 - Compounding the cube and octahedron


with the face center of the other so that their rotational axes and mirror planes


coincide.   As a result the octahedron is said to be the dual of the cube and v.v.  See

that the compounded polyhedra are created by raising the center point of their faces
until they can be connected by a straight line that bisects the intervening edge.

     Note that the faces of the cube and octahedron modeled in Fig. 7 interpenetrate

each other completely so that there is no ambiguity in the fact that the model was
compounded from two distinct and individual polyhedra.

page 5 of lesson

Exercise:  Demonstrate that the edges of the polyhedra are bisected

page 7 of lesson

and that straight lines connect the raised center points of their faces.

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