Overview
- Group
- SmallGroup(576,8589)
- Rank
- 5
- Schläfli Type
- {2,2,12,6}
- Vertices, edges, …
- 2, 2, 12, 36, 6
- Order of s0s1s2s3s4
- 12
- Order of s0s1s2s3s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
9-fold
12-fold
18-fold
Covers minimal covers in bold
2-fold
3-fold
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := (3,4);; s2 := ( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(23,32)(24,34)(25,33)(26,35)(27,37)(28,36)(29,38)(30,40)(31,39)(42,43)(45,46)(48,49)(51,52)(54,55)(57,58)(59,68)(60,70)(61,69)(62,71)(63,73)(64,72)(65,74)(66,76)(67,75);; s3 := ( 5,60)( 6,59)( 7,61)( 8,66)( 9,65)(10,67)(11,63)(12,62)(13,64)(14,69)(15,68)(16,70)(17,75)(18,74)(19,76)(20,72)(21,71)(22,73)(23,42)(24,41)(25,43)(26,48)(27,47)(28,49)(29,45)(30,44)(31,46)(32,51)(33,50)(34,52)(35,57)(36,56)(37,58)(38,54)(39,53)(40,55);; s4 := ( 5,44)( 6,46)( 7,45)( 8,41)( 9,43)(10,42)(11,47)(12,49)(13,48)(14,53)(15,55)(16,54)(17,50)(18,52)(19,51)(20,56)(21,58)(22,57)(23,62)(24,64)(25,63)(26,59)(27,61)(28,60)(29,65)(30,67)(31,66)(32,71)(33,73)(34,72)(35,68)(36,70)(37,69)(38,74)(39,76)(40,75);; poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s2*s3*s4*s2*s3*s2*s3*s4*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(76)!(1,2); s1 := Sym(76)!(3,4); s2 := Sym(76)!( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(23,32)(24,34)(25,33)(26,35)(27,37)(28,36)(29,38)(30,40)(31,39)(42,43)(45,46)(48,49)(51,52)(54,55)(57,58)(59,68)(60,70)(61,69)(62,71)(63,73)(64,72)(65,74)(66,76)(67,75); s3 := Sym(76)!( 5,60)( 6,59)( 7,61)( 8,66)( 9,65)(10,67)(11,63)(12,62)(13,64)(14,69)(15,68)(16,70)(17,75)(18,74)(19,76)(20,72)(21,71)(22,73)(23,42)(24,41)(25,43)(26,48)(27,47)(28,49)(29,45)(30,44)(31,46)(32,51)(33,50)(34,52)(35,57)(36,56)(37,58)(38,54)(39,53)(40,55); s4 := Sym(76)!( 5,44)( 6,46)( 7,45)( 8,41)( 9,43)(10,42)(11,47)(12,49)(13,48)(14,53)(15,55)(16,54)(17,50)(18,52)(19,51)(20,56)(21,58)(22,57)(23,62)(24,64)(25,63)(26,59)(27,61)(28,60)(29,65)(30,67)(31,66)(32,71)(33,73)(34,72)(35,68)(36,70)(37,69)(38,74)(39,76)(40,75); poly := sub<Sym(76)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s4*s2*s3*s2*s3*s4*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;