Twenty-four octants and six tetrahedra combine to build the cuboctahedron.

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cuboctahedron.gif (7265 bytes)

Volume = 3 octahedra + 8 tetrahedra

                      = 20 tetrahedra

                       = 5 octahedra

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Fig. 21 - Sectioning the cuboctahedron

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Required parts:  24 large triangles, 24 right triangles, 18 pinges

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     The ability to section these polyhedra and rearrange them into each other

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immediately and intuitively establishes a direct volumetric and dimensional

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relationship between them.  Further evidence of this is the fact that their respective

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volumes can be expressed as whole number multiples of the tetrahedron.

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Tetrahedron

Octahedron

Cube

Cuboctahedron

Tetrahedra

1

4

3

20

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page 16 of lesson

page 18 of lesson

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