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
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