Overview
- Group
- SmallGroup(1056,1022)
- Rank
- 5
- Schläfli Type
- {2,2,22,6}
- Vertices, edges, …
- 2, 2, 22, 66, 6
- 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 := ( 6,15)( 7,14)( 8,13)( 9,12)(10,11)(17,26)(18,25)(19,24)(20,23)(21,22)(28,37)(29,36)(30,35)(31,34)(32,33)(39,48)(40,47)(41,46)(42,45)(43,44)(50,59)(51,58)(52,57)(53,56)(54,55)(61,70)(62,69)(63,68)(64,67)(65,66);; s3 := ( 5, 6)( 7,15)( 8,14)( 9,13)(10,12)(16,28)(17,27)(18,37)(19,36)(20,35)(21,34)(22,33)(23,32)(24,31)(25,30)(26,29)(38,39)(40,48)(41,47)(42,46)(43,45)(49,61)(50,60)(51,70)(52,69)(53,68)(54,67)(55,66)(56,65)(57,64)(58,63)(59,62);; s4 := ( 5,49)( 6,50)( 7,51)( 8,52)( 9,53)(10,54)(11,55)(12,56)(13,57)(14,58)(15,59)(16,38)(17,39)(18,40)(19,41)(20,42)(21,43)(22,44)(23,45)(24,46)(25,47)(26,48)(27,60)(28,61)(29,62)(30,63)(31,64)(32,65)(33,66)(34,67)(35,68)(36,69)(37,70);; 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,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
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(70)!(1,2); s1 := Sym(70)!(3,4); s2 := Sym(70)!( 6,15)( 7,14)( 8,13)( 9,12)(10,11)(17,26)(18,25)(19,24)(20,23)(21,22)(28,37)(29,36)(30,35)(31,34)(32,33)(39,48)(40,47)(41,46)(42,45)(43,44)(50,59)(51,58)(52,57)(53,56)(54,55)(61,70)(62,69)(63,68)(64,67)(65,66); s3 := Sym(70)!( 5, 6)( 7,15)( 8,14)( 9,13)(10,12)(16,28)(17,27)(18,37)(19,36)(20,35)(21,34)(22,33)(23,32)(24,31)(25,30)(26,29)(38,39)(40,48)(41,47)(42,46)(43,45)(49,61)(50,60)(51,70)(52,69)(53,68)(54,67)(55,66)(56,65)(57,64)(58,63)(59,62); s4 := Sym(70)!( 5,49)( 6,50)( 7,51)( 8,52)( 9,53)(10,54)(11,55)(12,56)(13,57)(14,58)(15,59)(16,38)(17,39)(18,40)(19,41)(20,42)(21,43)(22,44)(23,45)(24,46)(25,47)(26,48)(27,60)(28,61)(29,62)(30,63)(31,64)(32,65)(33,66)(34,67)(35,68)(36,69)(37,70); 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, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 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 >;