
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. 

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Geometry rules!  Symmetry association by truncation 