Overview
- Group
- SmallGroup(1512,561)
- Rank
- 4
- Schläfli Type
- {2,6,42}
- Vertices, edges, …
- 2, 9, 189, 63
- Order of s0s1s2s3
- 42
- 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
7-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)(34,35)(37,38)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56)(58,59)(61,62)(64,65);; s2 := ( 6,21)( 7,22)( 8,23)( 9,18)(10,19)(11,20)(12,15)(13,16)(14,17)(24,47)(25,45)(26,46)(27,65)(28,63)(29,64)(30,62)(31,60)(32,61)(33,59)(34,57)(35,58)(36,56)(37,54)(38,55)(39,53)(40,51)(41,52)(42,50)(43,48)(44,49);; s3 := ( 3,27)( 4,29)( 5,28)( 6,24)( 7,26)( 8,25)( 9,42)(10,44)(11,43)(12,39)(13,41)(14,40)(15,36)(16,38)(17,37)(18,33)(19,35)(20,34)(21,30)(22,32)(23,31)(45,48)(46,50)(47,49)(51,63)(52,65)(53,64)(54,60)(55,62)(56,61)(58,59);; 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*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s3*s2*s1*s3*s2*s1*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(65)!(1,2); s1 := Sym(65)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)(34,35)(37,38)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56)(58,59)(61,62)(64,65); s2 := Sym(65)!( 6,21)( 7,22)( 8,23)( 9,18)(10,19)(11,20)(12,15)(13,16)(14,17)(24,47)(25,45)(26,46)(27,65)(28,63)(29,64)(30,62)(31,60)(32,61)(33,59)(34,57)(35,58)(36,56)(37,54)(38,55)(39,53)(40,51)(41,52)(42,50)(43,48)(44,49); s3 := Sym(65)!( 3,27)( 4,29)( 5,28)( 6,24)( 7,26)( 8,25)( 9,42)(10,44)(11,43)(12,39)(13,41)(14,40)(15,36)(16,38)(17,37)(18,33)(19,35)(20,34)(21,30)(22,32)(23,31)(45,48)(46,50)(47,49)(51,63)(52,65)(53,64)(54,60)(55,62)(56,61)(58,59); poly := sub<Sym(65)|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*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s3*s2*s1*s3*s2*s1*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 >;