Overview
- Group
- SmallGroup(24,6)
- Rank
- 2
- Schläfli Type
- {12}
- Vertices, edges, …
- 12, 12
- Order of s0s1
- 12
- Also known as
- dodecagon, {12}. if this polytope has another name.
Special Properties
- Universal
- Spherical
- Locally Spherical
- Orientable
- Self-Dual
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
Covers minimal covers in bold
2-fold
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83-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12);; s1 := ( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12);; poly := Group([s0,s1]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1");;
s0 := F.1;; s1 := F.2;;
rels := [ s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(12)!( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12); s1 := Sym(12)!( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12); poly := sub<Sym(12)|s0,s1>;
Finitely Presented Group Representation (Magma)
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References
None.
to this polytope.