Polymorf - Knowhwre - Truncating polyhedra

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


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.

Exercise: Explain how truncation destroys and

then restores the cubic symmetry of this model.

Page 10 Geometry rules! - Symmetry association by truncation