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 . . . . Table 1 - Ratio of tetrahedra to octahedra of space filling polyhedra

Back to Knowhere