Overview
- Group
- SmallGroup(864,4406)
- Rank
- 5
- Schläfli Type
- {3,2,12,6}
- Vertices, edges, …
- 3, 3, 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
Representations
Permutation Representation (GAP)
s0 := (2,3);; s1 := (1,2);; s2 := ( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(22,31)(23,33)(24,32)(25,34)(26,36)(27,35)(28,37)(29,39)(30,38)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(58,67)(59,69)(60,68)(61,70)(62,72)(63,71)(64,73)(65,75)(66,74);; s3 := ( 4,59)( 5,58)( 6,60)( 7,65)( 8,64)( 9,66)(10,62)(11,61)(12,63)(13,68)(14,67)(15,69)(16,74)(17,73)(18,75)(19,71)(20,70)(21,72)(22,41)(23,40)(24,42)(25,47)(26,46)(27,48)(28,44)(29,43)(30,45)(31,50)(32,49)(33,51)(34,56)(35,55)(36,57)(37,53)(38,52)(39,54);; s4 := ( 4,43)( 5,45)( 6,44)( 7,40)( 8,42)( 9,41)(10,46)(11,48)(12,47)(13,52)(14,54)(15,53)(16,49)(17,51)(18,50)(19,55)(20,57)(21,56)(22,61)(23,63)(24,62)(25,58)(26,60)(27,59)(28,64)(29,66)(30,65)(31,70)(32,72)(33,71)(34,67)(35,69)(36,68)(37,73)(38,75)(39,74);; 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*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,
s0*s1*s0*s1*s0*s1, 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(75)!(2,3); s1 := Sym(75)!(1,2); s2 := Sym(75)!( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(22,31)(23,33)(24,32)(25,34)(26,36)(27,35)(28,37)(29,39)(30,38)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(58,67)(59,69)(60,68)(61,70)(62,72)(63,71)(64,73)(65,75)(66,74); s3 := Sym(75)!( 4,59)( 5,58)( 6,60)( 7,65)( 8,64)( 9,66)(10,62)(11,61)(12,63)(13,68)(14,67)(15,69)(16,74)(17,73)(18,75)(19,71)(20,70)(21,72)(22,41)(23,40)(24,42)(25,47)(26,46)(27,48)(28,44)(29,43)(30,45)(31,50)(32,49)(33,51)(34,56)(35,55)(36,57)(37,53)(38,52)(39,54); s4 := Sym(75)!( 4,43)( 5,45)( 6,44)( 7,40)( 8,42)( 9,41)(10,46)(11,48)(12,47)(13,52)(14,54)(15,53)(16,49)(17,51)(18,50)(19,55)(20,57)(21,56)(22,61)(23,63)(24,62)(25,58)(26,60)(27,59)(28,64)(29,66)(30,65)(31,70)(32,72)(33,71)(34,67)(35,69)(36,68)(37,73)(38,75)(39,74); poly := sub<Sym(75)|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*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, s0*s1*s0*s1*s0*s1, s2*s3*s4*s2*s3*s2*s3*s4*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;