Tertiary space fillers

.
   Other polyhedra can fill space in combinations of three. .

spacecubetetrhomcube143x125res100transgif256.gif (9467 bytes)

spacetrunctetcuboctatruncocta162x125transgif256.gif (12049 bytes)

spacecubecuboctarhombicubocta140x125res100transgif256.gif (8859 bytes)

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

page 20 of lesson

page 22 of lesson

Back to Knowhere

Home page

Page 21    Geometry rules! - Space filling polyhedra

 

home   sitemap   products   Polywood   .networks   contact us   Knowhere   3Doodlings