
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 (1^{0}) polyhedra are 
doubled to create two frequency
(2^{0}) versions that are similar but larger. 



Vol. (2^{0})
= 4 tet. + 1 oct. 
Vol. (2^{0})
= 8 tet. + 6 oct. 
Vol. (2^{0})
= 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  1^{0}
and 2^{0} 
Fig. 22b  1^{0}
and 2^{0} 
Fig. 22c  1^{0}
and 2^{0} 
tetrahedra 
octahedra 
cubes 
. 


Required
parts (2^{0} 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 
. 
. 
. 

Exercise: Doubling the edge
length of a polyhedron increases 

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

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Geometry rules!  Volumetric relationship of polyhedra 