Symmetry association by truncation

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Another way that the symmetry elements of polyhedra can be associated is by

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truncation.   Truncation can be thought of as symmetrically slicing the vertices of

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the outer, circumscribing polyhedron to reveal the polyhedron inscribed inside it.

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Any of the models of inscribed polyhedra shown previously can be truncated.  For

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example slicing away four vertices of the cube uncovers the tetrahedron which can

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 Fig. 12 - Truncating the cube and then the tetrahedron yields the octahedron Required parts Large model (Fig. 12) Small model (see Fig. 9b) 20 large triangles, 48 right triangles 20 small triangles, 24 right triangles 84 pinges 48 pinges
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be further truncated creating the octahedron.  Observe that some elements of cubic

symmetry that are destroyed when the cube is truncated to create the tetrahedron

are restored when the tetrahedron is also truncated to make the octahedron.

Exercise:  Explain how truncation destroys and

then restores the cubic symmetry of this model.

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