Truncating the vertices of the icosahedron and dodecahedron generates three

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more Archimedean solids that are symmetrically identical to them: the truncated

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icosahedron, the truncated dodecahedron, and the icosidodecahedron.

Fig. 14a

Fig. 14b

Fig. 14c

Fig. 14d

Fig. 14e

Icosahedron

*Truncated

*Icosidodeca-

*Truncated

*Dodecahedron

icosahedron

hedron

dodecahedron

Required parts

20 triangles

240 triangles

90 triangles

140 triangles

60 triangles

30 pinges

330 pinges

120 pinges

60 squares

90 pinges

330 pinges

.
. .

Fig. 14 - Truncating the icosahedron and dodecahedron

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.

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Note:   As noted before squares and/or triangles are used to construct the

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pentagon, decagon, and dodecagon faces of some polyhedra to show

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symmetrically identical models of them, not their classical appearance.

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Exercise:  Truncating which polyhedra creates the triangle faces of the

icosidodecahedron?  How about the pentagon faces?  Why?

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