Overview
- Group
- SmallGroup(576,8654)
- Rank
- 5
- Schläfli Type
- {3,4,4,3}
- Vertices, edges, …
- 3, 12, 16, 12, 3
- Order of s0s1s2s3s4
- 6
- Order of s0s1s2s3s4s3s2s1
- 4
- Also known as
- {{3,4}3,{4,4}4,{4,3}3}. if this polytope has another name.
Special Properties
- Universal
- Non-Orientable
- Flat
- Self-Dual
Quotients maximal quotients in bold
No regular quotients.
Covers minimal covers in bold
2-fold
3-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 7, 8)(10,12);; s1 := ( 2, 4)( 6, 7)(11,12);; s2 := (1,4)(2,3)(5,6)(7,8);; s3 := ( 5, 9)( 6,11)( 7,12)( 8,10);; s4 := (1,5)(2,7)(3,8)(4,6);; poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1,
s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s2*s1*s0*s2*s1*s0*s2*s1,
s4*s2*s3*s4*s2*s3*s4*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(12)!( 2, 3)( 7, 8)(10,12); s1 := Sym(12)!( 2, 4)( 6, 7)(11,12); s2 := Sym(12)!(1,4)(2,3)(5,6)(7,8); s3 := Sym(12)!( 5, 9)( 6,11)( 7,12)( 8,10); s4 := Sym(12)!(1,5)(2,7)(3,8)(4,6); poly := sub<Sym(12)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3, s0*s2*s1*s0*s2*s1*s0*s2*s1, s4*s2*s3*s4*s2*s3*s4*s2*s3 >;
References
None.
to this polytope.