Truncating the Platonic solids to create the Archimedean solids

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Symmetrically truncating the vertices of the regular Platonic solids creates most

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of the semi-regular Archimedean solids.  This permits the symmetry of the latter to

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be associated with the former in a straightforward manner.  For example the cube

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and octahedron can be progressively truncated to yield the cuboctahedron. The

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 . . .

Fig. 13a

Fig. 13b

Fig. 13c

Fig. 13d

Fig. 13e

Truncated cube

Truncated

Cuboctahedron

Truncated

Octahedron

in a cube

cube

octahedron

Required parts

8 large triangles

8 triangles

48 triangles

8 triangles

6 large squares

6 squares

6 squares

12 pinges

24 rectangles

24 pinges

84 pinges

24 right triangles (48 for 13a)

96 pinges (120 for 13a)

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Fig. 13 -   Truncating the cube and octahedron to make the cuboctahedron

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truncated cube and the truncated octahedron are generated in the process.  Since

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each vertex of the polyhedra are symmetrically sliced off the resulting polyhedra

retain the same symmetry elements as the original.

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Exercise: Truncating the vertices of  which polyhedron produces the triangle

faces of the cuboctahedron?  Which one produces the square's?  Why?

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