Symmetry association by truncation


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


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


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


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


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


octahedron.gif (12089 bytes)

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




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.

page 9 of lesson

Exercise:  Explain how truncation destroys and

page 11 of lesson

then restores the cubic symmetry of this model.

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