Overview
- Group
- SmallGroup(1632,1195)
- Rank
- 4
- Schläfli Type
- {2,68,6}
- Vertices, edges, …
- 2, 68, 204, 6
- Order of s0s1s2s3
- 102
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
17-fold
34-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 3, 5)( 4, 6)( 7,69)( 8,70)( 9,67)(10,68)(11,65)(12,66)(13,63)(14,64)(15,61)(16,62)(17,59)(18,60)(19,57)(20,58)(21,55)(22,56)(23,53)(24,54)(25,51)(26,52)(27,49)(28,50)(29,47)(30,48)(31,45)(32,46)(33,43)(34,44)(35,41)(36,42)(37,39)(38,40);; s2 := ( 3, 7)( 4, 9)( 5, 8)( 6,10)(11,67)(12,69)(13,68)(14,70)(15,63)(16,65)(17,64)(18,66)(19,59)(20,61)(21,60)(22,62)(23,55)(24,57)(25,56)(26,58)(27,51)(28,53)(29,52)(30,54)(31,47)(32,49)(33,48)(34,50)(35,43)(36,45)(37,44)(38,46)(40,41);; s3 := ( 4, 6)( 8,10)(12,14)(16,18)(20,22)(24,26)(28,30)(32,34)(36,38)(40,42)(44,46)(48,50)(52,54)(56,58)(60,62)(64,66)(68,70);; 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*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2,
s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2,
s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(70)!(1,2); s1 := Sym(70)!( 3, 5)( 4, 6)( 7,69)( 8,70)( 9,67)(10,68)(11,65)(12,66)(13,63)(14,64)(15,61)(16,62)(17,59)(18,60)(19,57)(20,58)(21,55)(22,56)(23,53)(24,54)(25,51)(26,52)(27,49)(28,50)(29,47)(30,48)(31,45)(32,46)(33,43)(34,44)(35,41)(36,42)(37,39)(38,40); s2 := Sym(70)!( 3, 7)( 4, 9)( 5, 8)( 6,10)(11,67)(12,69)(13,68)(14,70)(15,63)(16,65)(17,64)(18,66)(19,59)(20,61)(21,60)(22,62)(23,55)(24,57)(25,56)(26,58)(27,51)(28,53)(29,52)(30,54)(31,47)(32,49)(33,48)(34,50)(35,43)(36,45)(37,44)(38,46)(40,41); s3 := Sym(70)!( 4, 6)( 8,10)(12,14)(16,18)(20,22)(24,26)(28,30)(32,34)(36,38)(40,42)(44,46)(48,50)(52,54)(56,58)(60,62)(64,66)(68,70); 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*s2*s3*s2*s3*s2*s3*s2*s3, s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2, s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2, s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1 >;