Overview
- Group
- SmallGroup(1320,168)
- Rank
- 4
- Schläfli Type
- {11,2,30}
- Vertices, edges, …
- 11, 11, 30, 30
- Order of s0s1s2s3
- 330
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
5-fold
6-fold
10-fold
15-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11);; s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10);; s2 := (14,15)(16,17)(18,19)(20,21)(22,25)(23,24)(26,27)(28,31)(29,30)(32,33)(34,37)(35,36)(38,41)(39,40);; s3 := (12,28)(13,22)(14,20)(15,30)(16,18)(17,38)(19,24)(21,34)(23,32)(25,40)(26,29)(27,39)(31,36)(33,35)(37,41);; poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(41)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11); s1 := Sym(41)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10); s2 := Sym(41)!(14,15)(16,17)(18,19)(20,21)(22,25)(23,24)(26,27)(28,31)(29,30)(32,33)(34,37)(35,36)(38,41)(39,40); s3 := Sym(41)!(12,28)(13,22)(14,20)(15,30)(16,18)(17,38)(19,24)(21,34)(23,32)(25,40)(26,29)(27,39)(31,36)(33,35)(37,41); poly := sub<Sym(41)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;