|
Tertiary
space fillers |
. |
| Other polyhedra
can fill space in combinations of three. |
. |
 |
 |
 |
Fig. 28 -
Tetrahedra/ |
Fig. 29 -
Cuboctahedra/ |
Fig. 30 -
Cubes/ |
rhombicuboctahedra/ |
truncated
octahedra/ |
rhombicuboctahedra/ |
cubes space
filling |
truncated
tetrahedra |
cuboctahedra |
| . |
|
|
Combination
ratio: 2/1/1 |
1/1/2 |
3/1/1 |
|
. |
| . |
. |
Another requirement for these polyhedra to be space fillers is that they |
. |
pack together so their combined volumes, when
expressed in tetrahedral |
. |
and octahedral equivalents,
maintain a strict ratio of two tetrahedra to one |
. |
octahedron. This
presumes of course that the edges of all the polyhedra
are |
. |
|
the same
length and therefore
can be meaningfully compared. |
| . |
Figure |
Polyhedra |
Combined |
Tetra. |
Octa. |
Tetra./octa. |
. |
. |
ratio |
. |
. |
ratio |
23 |
cubes |
uniary |
1 |
1/2 |
2/1 |
24 |
truncated
octahedra |
uniary |
32 |
16 |
2/1 |
25 |
tetrahedra/octahedra |
2/1 |
2 |
1 |
2/1 |
26 |
tetra./trunc.
tetrahedra |
1/1 |
8 |
4 |
2/1 |
27 |
octahedra/cuboctahedra |
1/1 |
8 |
4 |
2/1 |
29 |
cuboctahedra/ |
1/1/2 |
54 |
27 |
2/1 |
. |
truncated
octahedra/ |
. |
. |
. |
. |
. |
truncated
tetrahedra |
. |
. |
. |
. |
|
|
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Table 1 - Ratio of tetrahedra to octahedra of space filling polyhedra |
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Geometry rules! - Space filling polyhedra |
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