Overview
- Group
- SmallGroup(1512,561)
- Rank
- 4
- Schläfli Type
- {2,21,6}
- Vertices, edges, …
- 2, 63, 189, 18
- Order of s0s1s2s3
- 42
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
3-fold
7-fold
9-fold
21-fold
27-fold
63-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 6,21)( 7,22)( 8,23)( 9,18)(10,19)(11,20)(12,15)(13,16)(14,17)(24,45)(25,46)(26,47)(27,63)(28,64)(29,65)(30,60)(31,61)(32,62)(33,57)(34,58)(35,59)(36,54)(37,55)(38,56)(39,51)(40,52)(41,53)(42,48)(43,49)(44,50);; s2 := ( 3,28)( 4,29)( 5,27)( 6,25)( 7,26)( 8,24)( 9,43)(10,44)(11,42)(12,40)(13,41)(14,39)(15,37)(16,38)(17,36)(18,34)(19,35)(20,33)(21,31)(22,32)(23,30)(45,48)(46,49)(47,50)(51,63)(52,64)(53,65)(54,60)(55,61)(56,62);; s3 := ( 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);; 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*s3*s2*s1*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*s3*s2*s3*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(65)!(1,2); s1 := Sym(65)!( 6,21)( 7,22)( 8,23)( 9,18)(10,19)(11,20)(12,15)(13,16)(14,17)(24,45)(25,46)(26,47)(27,63)(28,64)(29,65)(30,60)(31,61)(32,62)(33,57)(34,58)(35,59)(36,54)(37,55)(38,56)(39,51)(40,52)(41,53)(42,48)(43,49)(44,50); s2 := Sym(65)!( 3,28)( 4,29)( 5,27)( 6,25)( 7,26)( 8,24)( 9,43)(10,44)(11,42)(12,40)(13,41)(14,39)(15,37)(16,38)(17,36)(18,34)(19,35)(20,33)(21,31)(22,32)(23,30)(45,48)(46,49)(47,50)(51,63)(52,64)(53,65)(54,60)(55,61)(56,62); s3 := 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); 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*s3*s2*s1*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*s3*s2*s3*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;