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