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

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

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jam201202octacubeaniwhtbkgrnd95x95gif128.gif (6800 bytes)

octacubecomanitrans107x100res100gif255.gif (14325 bytes)

Fig. 7a - Compound cube/

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

octahedron

symmetry of cube/octahedron

Required parts

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

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Fig. 7 - Compounding the cube and octahedron

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

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

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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

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