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