Overview
- Group
- SmallGroup(864,4368)
- 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 := ( 4,40)( 5,42)( 6,41)( 7,46)( 8,48)( 9,47)(10,43)(11,45)(12,44)(13,49)(14,51)(15,50)(16,55)(17,57)(18,56)(19,52)(20,54)(21,53)(22,67)(23,69)(24,68)(25,73)(26,75)(27,74)(28,70)(29,72)(30,71)(31,58)(32,60)(33,59)(34,64)(35,66)(36,65)(37,61)(38,63)(39,62);; s3 := ( 4,62)( 5,61)( 6,63)( 7,59)( 8,58)( 9,60)(10,65)(11,64)(12,66)(13,71)(14,70)(15,72)(16,68)(17,67)(18,69)(19,74)(20,73)(21,75)(22,44)(23,43)(24,45)(25,41)(26,40)(27,42)(28,47)(29,46)(30,48)(31,53)(32,52)(33,54)(34,50)(35,49)(36,51)(37,56)(38,55)(39,57);; s4 := ( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)(35,36)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(59,60)(62,63)(65,66)(68,69)(71,72)(74,75);; 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*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, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3,
s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(75)!(2,3); s1 := Sym(75)!(1,2); s2 := Sym(75)!( 4,40)( 5,42)( 6,41)( 7,46)( 8,48)( 9,47)(10,43)(11,45)(12,44)(13,49)(14,51)(15,50)(16,55)(17,57)(18,56)(19,52)(20,54)(21,53)(22,67)(23,69)(24,68)(25,73)(26,75)(27,74)(28,70)(29,72)(30,71)(31,58)(32,60)(33,59)(34,64)(35,66)(36,65)(37,61)(38,63)(39,62); s3 := Sym(75)!( 4,62)( 5,61)( 6,63)( 7,59)( 8,58)( 9,60)(10,65)(11,64)(12,66)(13,71)(14,70)(15,72)(16,68)(17,67)(18,69)(19,74)(20,73)(21,75)(22,44)(23,43)(24,45)(25,41)(26,40)(27,42)(28,47)(29,46)(30,48)(31,53)(32,52)(33,54)(34,50)(35,49)(36,51)(37,56)(38,55)(39,57); s4 := Sym(75)!( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)(35,36)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(59,60)(62,63)(65,66)(68,69)(71,72)(74,75); 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, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;