Overview
- Group
- SmallGroup(1920,236171)
- Rank
- 6
- Schläfli Type
- {2,2,2,4,30}
- Vertices, edges, …
- 2, 2, 2, 4, 60, 30
- Order of s0s1s2s3s4s5
- 60
- Order of s0s1s2s3s4s5s4s3s2s1
- 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
5-fold
6-fold
10-fold
12-fold
15-fold
20-fold
30-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := (3,4);; s2 := (5,6);; s3 := (37,52)(38,53)(39,54)(40,55)(41,56)(42,57)(43,58)(44,59)(45,60)(46,61)(47,62)(48,63)(49,64)(50,65)(51,66);; s4 := ( 7,37)( 8,41)( 9,40)(10,39)(11,38)(12,47)(13,51)(14,50)(15,49)(16,48)(17,42)(18,46)(19,45)(20,44)(21,43)(22,52)(23,56)(24,55)(25,54)(26,53)(27,62)(28,66)(29,65)(30,64)(31,63)(32,57)(33,61)(34,60)(35,59)(36,58);; s5 := ( 7,13)( 8,12)( 9,16)(10,15)(11,14)(17,18)(19,21)(22,28)(23,27)(24,31)(25,30)(26,29)(32,33)(34,36)(37,43)(38,42)(39,46)(40,45)(41,44)(47,48)(49,51)(52,58)(53,57)(54,61)(55,60)(56,59)(62,63)(64,66);; poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s3*s4*s3*s4*s3*s4*s3*s4,
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(66)!(1,2); s1 := Sym(66)!(3,4); s2 := Sym(66)!(5,6); s3 := Sym(66)!(37,52)(38,53)(39,54)(40,55)(41,56)(42,57)(43,58)(44,59)(45,60)(46,61)(47,62)(48,63)(49,64)(50,65)(51,66); s4 := Sym(66)!( 7,37)( 8,41)( 9,40)(10,39)(11,38)(12,47)(13,51)(14,50)(15,49)(16,48)(17,42)(18,46)(19,45)(20,44)(21,43)(22,52)(23,56)(24,55)(25,54)(26,53)(27,62)(28,66)(29,65)(30,64)(31,63)(32,57)(33,61)(34,60)(35,59)(36,58); s5 := Sym(66)!( 7,13)( 8,12)( 9,16)(10,15)(11,14)(17,18)(19,21)(22,28)(23,27)(24,31)(25,30)(26,29)(32,33)(34,36)(37,43)(38,42)(39,46)(40,45)(41,44)(47,48)(49,51)(52,58)(53,57)(54,61)(55,60)(56,59)(62,63)(64,66); poly := sub<Sym(66)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, s3*s4*s3*s4*s3*s4*s3*s4, s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;