Overview
- Group
- SmallGroup(1056,1022)
- Rank
- 5
- Schläfli Type
- {2,2,6,22}
- Vertices, edges, …
- 2, 2, 6, 66, 22
- Order of s0s1s2s3s4
- 66
- Order of s0s1s2s3s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
3-fold
6-fold
11-fold
22-fold
33-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := (3,4);; s2 := (16,27)(17,28)(18,29)(19,30)(20,31)(21,32)(22,33)(23,34)(24,35)(25,36)(26,37)(49,60)(50,61)(51,62)(52,63)(53,64)(54,65)(55,66)(56,67)(57,68)(58,69)(59,70);; s3 := ( 5,16)( 6,26)( 7,25)( 8,24)( 9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)(28,37)(29,36)(30,35)(31,34)(32,33)(38,49)(39,59)(40,58)(41,57)(42,56)(43,55)(44,54)(45,53)(46,52)(47,51)(48,50)(61,70)(62,69)(63,68)(64,67)(65,66);; s4 := ( 5,39)( 6,38)( 7,48)( 8,47)( 9,46)(10,45)(11,44)(12,43)(13,42)(14,41)(15,40)(16,50)(17,49)(18,59)(19,58)(20,57)(21,56)(22,55)(23,54)(24,53)(25,52)(26,51)(27,61)(28,60)(29,70)(30,69)(31,68)(32,67)(33,66)(34,65)(35,64)(36,63)(37,62);; 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*s1*s0*s1,
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(70)!(1,2); s1 := Sym(70)!(3,4); s2 := Sym(70)!(16,27)(17,28)(18,29)(19,30)(20,31)(21,32)(22,33)(23,34)(24,35)(25,36)(26,37)(49,60)(50,61)(51,62)(52,63)(53,64)(54,65)(55,66)(56,67)(57,68)(58,69)(59,70); s3 := Sym(70)!( 5,16)( 6,26)( 7,25)( 8,24)( 9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)(28,37)(29,36)(30,35)(31,34)(32,33)(38,49)(39,59)(40,58)(41,57)(42,56)(43,55)(44,54)(45,53)(46,52)(47,51)(48,50)(61,70)(62,69)(63,68)(64,67)(65,66); s4 := Sym(70)!( 5,39)( 6,38)( 7,48)( 8,47)( 9,46)(10,45)(11,44)(12,43)(13,42)(14,41)(15,40)(16,50)(17,49)(18,59)(19,58)(20,57)(21,56)(22,55)(23,54)(24,53)(25,52)(26,51)(27,61)(28,60)(29,70)(30,69)(31,68)(32,67)(33,66)(34,65)(35,64)(36,63)(37,62); poly := sub<Sym(70)|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*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;