Overview
- Group
- SmallGroup(504,192)
- Rank
- 4
- Schläfli Type
- {6,21,2}
- Vertices, edges, …
- 6, 63, 21, 2
- 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
Covers minimal covers in bold
2-fold
3-fold
Representations
Permutation Representation (GAP)
s0 := (22,43)(23,44)(24,45)(25,46)(26,47)(27,48)(28,49)(29,50)(30,51)(31,52)(32,53)(33,54)(34,55)(35,56)(36,57)(37,58)(38,59)(39,60)(40,61)(41,62)(42,63);; s1 := ( 1,22)( 2,28)( 3,27)( 4,26)( 5,25)( 6,24)( 7,23)( 8,36)( 9,42)(10,41)(11,40)(12,39)(13,38)(14,37)(15,29)(16,35)(17,34)(18,33)(19,32)(20,31)(21,30)(44,49)(45,48)(46,47)(50,57)(51,63)(52,62)(53,61)(54,60)(55,59)(56,58);; s2 := ( 1, 9)( 2, 8)( 3,14)( 4,13)( 5,12)( 6,11)( 7,10)(15,16)(17,21)(18,20)(22,51)(23,50)(24,56)(25,55)(26,54)(27,53)(28,52)(29,44)(30,43)(31,49)(32,48)(33,47)(34,46)(35,45)(36,58)(37,57)(38,63)(39,62)(40,61)(41,60)(42,59);; s3 := (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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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)!(22,43)(23,44)(24,45)(25,46)(26,47)(27,48)(28,49)(29,50)(30,51)(31,52)(32,53)(33,54)(34,55)(35,56)(36,57)(37,58)(38,59)(39,60)(40,61)(41,62)(42,63); s1 := Sym(65)!( 1,22)( 2,28)( 3,27)( 4,26)( 5,25)( 6,24)( 7,23)( 8,36)( 9,42)(10,41)(11,40)(12,39)(13,38)(14,37)(15,29)(16,35)(17,34)(18,33)(19,32)(20,31)(21,30)(44,49)(45,48)(46,47)(50,57)(51,63)(52,62)(53,61)(54,60)(55,59)(56,58); s2 := Sym(65)!( 1, 9)( 2, 8)( 3,14)( 4,13)( 5,12)( 6,11)( 7,10)(15,16)(17,21)(18,20)(22,51)(23,50)(24,56)(25,55)(26,54)(27,53)(28,52)(29,44)(30,43)(31,49)(32,48)(33,47)(34,46)(35,45)(36,58)(37,57)(38,63)(39,62)(40,61)(41,60)(42,59); s3 := Sym(65)!(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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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 >;