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

 .

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

 .
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.

tetrahedron.gif (5386 bytes)

octahedron.gif (7015 bytes)

cube.gif (9681 bytes)

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
.
. .

Fig. 22 - Sectioning two frequency polyhedra

 .
. .

page 17 of lesson

Exercise:  Doubling the edge length of a polyhedron increases

page 19 of lesson

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

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