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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 |
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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. |
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Exercise: Explain how truncation
destroys and |
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then restores the cubic symmetry of
this model. |
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Geometry rules! - Symmetry association by truncation |