Overview
- Group
- SmallGroup(1008,922)
- Rank
- 4
- Schläfli Type
- {2,6,42}
- Vertices, edges, …
- 2, 6, 126, 42
- 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 := (10,17)(11,18)(12,19)(13,20)(14,21)(15,22)(16,23)(24,45)(25,46)(26,47)(27,48)(28,49)(29,50)(30,51)(31,59)(32,60)(33,61)(34,62)(35,63)(36,64)(37,65)(38,52)(39,53)(40,54)(41,55)(42,56)(43,57)(44,58);; s2 := ( 3,31)( 4,37)( 5,36)( 6,35)( 7,34)( 8,33)( 9,32)(10,24)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,38)(18,44)(19,43)(20,42)(21,41)(22,40)(23,39)(45,52)(46,58)(47,57)(48,56)(49,55)(50,54)(51,53)(60,65)(61,64)(62,63);; s3 := ( 3, 4)( 5, 9)( 6, 8)(10,18)(11,17)(12,23)(13,22)(14,21)(15,20)(16,19)(24,25)(26,30)(27,29)(31,39)(32,38)(33,44)(34,43)(35,42)(36,41)(37,40)(45,46)(47,51)(48,50)(52,60)(53,59)(54,65)(55,64)(56,63)(57,62)(58,61);; 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*s2*s3*s1*s2*s1*s2*s3*s2*s3*s1*s2,
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(65)!(1,2); s1 := Sym(65)!(10,17)(11,18)(12,19)(13,20)(14,21)(15,22)(16,23)(24,45)(25,46)(26,47)(27,48)(28,49)(29,50)(30,51)(31,59)(32,60)(33,61)(34,62)(35,63)(36,64)(37,65)(38,52)(39,53)(40,54)(41,55)(42,56)(43,57)(44,58); s2 := Sym(65)!( 3,31)( 4,37)( 5,36)( 6,35)( 7,34)( 8,33)( 9,32)(10,24)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,38)(18,44)(19,43)(20,42)(21,41)(22,40)(23,39)(45,52)(46,58)(47,57)(48,56)(49,55)(50,54)(51,53)(60,65)(61,64)(62,63); s3 := Sym(65)!( 3, 4)( 5, 9)( 6, 8)(10,18)(11,17)(12,23)(13,22)(14,21)(15,20)(16,19)(24,25)(26,30)(27,29)(31,39)(32,38)(33,44)(34,43)(35,42)(36,41)(37,40)(45,46)(47,51)(48,50)(52,60)(53,59)(54,65)(55,64)(56,63)(57,62)(58,61); 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*s2*s3*s1*s2*s1*s2*s3*s2*s3*s1*s2, s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2 >;