Overview
- Group
- SmallGroup(528,169)
- Rank
- 4
- Schläfli Type
- {2,66,2}
- Vertices, edges, …
- 2, 66, 66, 2
- Order of s0s1s2s3
- 66
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
- Self-Dual
Quotients maximal quotients in bold
2-fold
3-fold
6-fold
11-fold
22-fold
33-fold
Covers minimal covers in bold
2-fold
3-fold
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4,13)( 5,12)( 6,11)( 7,10)( 8, 9)(14,25)(15,35)(16,34)(17,33)(18,32)(19,31)(20,30)(21,29)(22,28)(23,27)(24,26)(37,46)(38,45)(39,44)(40,43)(41,42)(47,58)(48,68)(49,67)(50,66)(51,65)(52,64)(53,63)(54,62)(55,61)(56,60)(57,59);; s2 := ( 3,48)( 4,47)( 5,57)( 6,56)( 7,55)( 8,54)( 9,53)(10,52)(11,51)(12,50)(13,49)(14,37)(15,36)(16,46)(17,45)(18,44)(19,43)(20,42)(21,41)(22,40)(23,39)(24,38)(25,59)(26,58)(27,68)(28,67)(29,66)(30,65)(31,64)(32,63)(33,62)(34,61)(35,60);; s3 := (69,70);; 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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(70)!(1,2); s1 := Sym(70)!( 4,13)( 5,12)( 6,11)( 7,10)( 8, 9)(14,25)(15,35)(16,34)(17,33)(18,32)(19,31)(20,30)(21,29)(22,28)(23,27)(24,26)(37,46)(38,45)(39,44)(40,43)(41,42)(47,58)(48,68)(49,67)(50,66)(51,65)(52,64)(53,63)(54,62)(55,61)(56,60)(57,59); s2 := Sym(70)!( 3,48)( 4,47)( 5,57)( 6,56)( 7,55)( 8,54)( 9,53)(10,52)(11,51)(12,50)(13,49)(14,37)(15,36)(16,46)(17,45)(18,44)(19,43)(20,42)(21,41)(22,40)(23,39)(24,38)(25,59)(26,58)(27,68)(28,67)(29,66)(30,65)(31,64)(32,63)(33,62)(34,61)(35,60); s3 := Sym(70)!(69,70); poly := sub<Sym(70)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;