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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. |
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 |
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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 |
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Fig. 22a - 10
and 20 |
Fig. 22b - 10
and 20 |
Fig. 22c - 10
and 20 |
tetrahedra |
octahedra |
cubes |
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Required
parts (20 models) |
20 triangles |
48 large
triangles |
24 large
triangles |
24 pinges |
48 right
triangles |
48 right
triangles |
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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 |
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its volume by what factor? What
about its surface area? |
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Page 18
Geometry rules! - Volumetric relationship of polyhedra |