Overview
- Group
- SmallGroup(1008,922)
- Rank
- 4
- Schläfli Type
- {2,42,6}
- Vertices, edges, …
- 2, 42, 126, 6
- 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
14-fold
18-fold
21-fold
42-fold
63-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 9)( 5, 8)( 6, 7)(10,17)(11,23)(12,22)(13,21)(14,20)(15,19)(16,18)(25,30)(26,29)(27,28)(31,38)(32,44)(33,43)(34,42)(35,41)(36,40)(37,39)(46,51)(47,50)(48,49)(52,59)(53,65)(54,64)(55,63)(56,62)(57,61)(58,60);; s2 := ( 3,11)( 4,10)( 5,16)( 6,15)( 7,14)( 8,13)( 9,12)(17,18)(19,23)(20,22)(24,53)(25,52)(26,58)(27,57)(28,56)(29,55)(30,54)(31,46)(32,45)(33,51)(34,50)(35,49)(36,48)(37,47)(38,60)(39,59)(40,65)(41,64)(42,63)(43,62)(44,61);; s3 := ( 3,24)( 4,25)( 5,26)( 6,27)( 7,28)( 8,29)( 9,30)(10,38)(11,39)(12,40)(13,41)(14,42)(15,43)(16,44)(17,31)(18,32)(19,33)(20,34)(21,35)(22,36)(23,37)(52,59)(53,60)(54,61)(55,62)(56,63)(57,64)(58,65);; 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,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s2*s3*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s3*s2*s1*s2*s1*s2*s1*s2*s1*s3*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(65)!(1,2); s1 := Sym(65)!( 4, 9)( 5, 8)( 6, 7)(10,17)(11,23)(12,22)(13,21)(14,20)(15,19)(16,18)(25,30)(26,29)(27,28)(31,38)(32,44)(33,43)(34,42)(35,41)(36,40)(37,39)(46,51)(47,50)(48,49)(52,59)(53,65)(54,64)(55,63)(56,62)(57,61)(58,60); s2 := Sym(65)!( 3,11)( 4,10)( 5,16)( 6,15)( 7,14)( 8,13)( 9,12)(17,18)(19,23)(20,22)(24,53)(25,52)(26,58)(27,57)(28,56)(29,55)(30,54)(31,46)(32,45)(33,51)(34,50)(35,49)(36,48)(37,47)(38,60)(39,59)(40,65)(41,64)(42,63)(43,62)(44,61); s3 := Sym(65)!( 3,24)( 4,25)( 5,26)( 6,27)( 7,28)( 8,29)( 9,30)(10,38)(11,39)(12,40)(13,41)(14,42)(15,43)(16,44)(17,31)(18,32)(19,33)(20,34)(21,35)(22,36)(23,37)(52,59)(53,60)(54,61)(55,62)(56,63)(57,64)(58,65); 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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s2*s3*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s3*s2*s1*s2*s1*s2*s1*s2*s1*s3*s2*s1*s2*s1*s2 >;