Related Polyhedra and Tilings
The pentagonal icositetrahedron is one of a family of duals to the uniform polyhedra related to the cube and regular octahedron.
| {4,3} | t0,1{4,3} | t1{4,3} | t0,1{3,4} | {3,4} | t0,2{4,3} | t0,1,2{4,3} | s{4,3} | h{4,3} | h1,2{4,3} |
|---|---|---|---|---|---|---|---|---|---|
| Duals to uniform polyhedra | |||||||||
| {3,4} | f0,1{4,3} | f1{4,3} | f0,1{3,4} | {4,3} | f0,2{4,3} | f0,1,2{4,3} | ds{4,3} | hf{4,3} | hf1,2{4,3} |
This polyhedron is topologically related as a part of sequence of polyhedra and tilings of pentagons with face configurations (V3.3.3.3.n). (The sequence progresses into tilings the hyperbolic plane to any n.) These face-transitive figures have (n32) rotational symmetry.
| Symmetry | 232 + D3 |
332 + T |
432 + O |
532 + I |
632 + P6 |
732 + |
832 + |
|---|---|---|---|---|---|---|---|
| Order | 6 | 12 | 24 | 60 | ∞ | ||
| Snub figure |
3.3.3.3.2 |
3.3.3.3.3 |
3.3.3.3.4 |
3.3.3.3.5 |
3.3.3.3.6 |
3.3.3.3.7 |
3.3.3.3.8 |
| Coxeter Schläfli |
s{2,3} |
s{3,3} |
s{4,3} |
s{5,3} |
s{6,3} |
s{7,3} |
s{8,3} |
| Snub dual figure |
V3.3.3.3.2 |
V3.3.3.3.3 |
V3.3.3.3.4 |
V3.3.3.3.5 |
V3.3.3.3.6 |
V3.3.3.3.7 |
|
| Coxeter | |||||||
Read more about this topic: Pentagonal Icositetrahedron
Famous quotes containing the word related:
“Just as a new scientific discovery manifests something that was already latent in the order of nature, and at the same time is logically related to the total structure of the existing science, so the new poem manifests something that was already latent in the order of words.”
—Northrop Frye (b. 1912)