Overview
- Group
- SmallGroup(576,8545)
- Rank
- 5
- Schläfli Type
- {2,2,6,12}
- Vertices, edges, …
- 2, 2, 6, 36, 12
- 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
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)(24,25)(27,28)(30,31)(33,34)(36,37)(39,40)(42,43)(45,46)(48,49)(51,52)(54,55)(57,58)(60,61)(63,64)(66,67)(69,70)(72,73)(75,76);; s3 := ( 5,42)( 6,41)( 7,43)( 8,48)( 9,47)(10,49)(11,45)(12,44)(13,46)(14,51)(15,50)(16,52)(17,57)(18,56)(19,58)(20,54)(21,53)(22,55)(23,69)(24,68)(25,70)(26,75)(27,74)(28,76)(29,72)(30,71)(31,73)(32,60)(33,59)(34,61)(35,66)(36,65)(37,67)(38,63)(39,62)(40,64);; s4 := ( 5,62)( 6,63)( 7,64)( 8,59)( 9,60)(10,61)(11,65)(12,66)(13,67)(14,71)(15,72)(16,73)(17,68)(18,69)(19,70)(20,74)(21,75)(22,76)(23,44)(24,45)(25,46)(26,41)(27,42)(28,43)(29,47)(30,48)(31,49)(32,53)(33,54)(34,55)(35,50)(36,51)(37,52)(38,56)(39,57)(40,58);; 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*s3*s2*s3*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*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)(24,25)(27,28)(30,31)(33,34)(36,37)(39,40)(42,43)(45,46)(48,49)(51,52)(54,55)(57,58)(60,61)(63,64)(66,67)(69,70)(72,73)(75,76); s3 := Sym(76)!( 5,42)( 6,41)( 7,43)( 8,48)( 9,47)(10,49)(11,45)(12,44)(13,46)(14,51)(15,50)(16,52)(17,57)(18,56)(19,58)(20,54)(21,53)(22,55)(23,69)(24,68)(25,70)(26,75)(27,74)(28,76)(29,72)(30,71)(31,73)(32,60)(33,59)(34,61)(35,66)(36,65)(37,67)(38,63)(39,62)(40,64); s4 := Sym(76)!( 5,62)( 6,63)( 7,64)( 8,59)( 9,60)(10,61)(11,65)(12,66)(13,67)(14,71)(15,72)(16,73)(17,68)(18,69)(19,70)(20,74)(21,75)(22,76)(23,44)(24,45)(25,46)(26,41)(27,42)(28,43)(29,47)(30,48)(31,49)(32,53)(33,54)(34,55)(35,50)(36,51)(37,52)(38,56)(39,57)(40,58); 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*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;