Even larger models can be sectioned to demonstrate the concepts of similarity and

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the geometric increase of surface area and volume with increasing edge lengths.  In

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the following models the edge lengths of the single frequency (10) polyhedra are
doubled to create two frequency (20) versions that are similar but larger.
 Vol. (20) = 4 tet. + 1 oct. Vol. (20) = 8 tet. + 6 oct. Vol. (20) = 8 tet. + 4 oct. = 8 tetrahedra = 32 tetrahedra = 24 tetrahedra = 2 octahedra = 8 octahedra = 6 octahedra Surface = 16 triangles Surface = 32 triangles Surface = 24 squares . Fig. 22a - 10 and 20 Fig. 22b - 10 and 20 Fig. 22c - 10 and 20 tetrahedra octahedra cubes . Required parts (20 models) 20 triangles 48 large triangles 24 large triangles 24 pinges 48 right triangles 48 right triangles 72 pinges 66 pinges
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Fig. 22 - Sectioning two frequency polyhedra

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Exercise:  Doubling the edge length of a polyhedron increases

its volume by what factor?  What about its surface area?

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