Overview
- Group
- SmallGroup(1920,236182)
- Rank
- 6
- Schläfli Type
- {2,2,2,12,10}
- Vertices, edges, …
- 2, 2, 2, 12, 60, 10
- 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
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 := (12,17)(13,18)(14,19)(15,20)(16,21)(27,32)(28,33)(29,34)(30,35)(31,36)(37,52)(38,53)(39,54)(40,55)(41,56)(42,62)(43,63)(44,64)(45,65)(46,66)(47,57)(48,58)(49,59)(50,60)(51,61);; s4 := ( 7,42)( 8,46)( 9,45)(10,44)(11,43)(12,37)(13,41)(14,40)(15,39)(16,38)(17,47)(18,51)(19,50)(20,49)(21,48)(22,57)(23,61)(24,60)(25,59)(26,58)(27,52)(28,56)(29,55)(30,54)(31,53)(32,62)(33,66)(34,65)(35,64)(36,63);; s5 := ( 7, 8)( 9,11)(12,13)(14,16)(17,18)(19,21)(22,23)(24,26)(27,28)(29,31)(32,33)(34,36)(37,38)(39,41)(42,43)(44,46)(47,48)(49,51)(52,53)(54,56)(57,58)(59,61)(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*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,
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(66)!(1,2); s1 := Sym(66)!(3,4); s2 := Sym(66)!(5,6); s3 := Sym(66)!(12,17)(13,18)(14,19)(15,20)(16,21)(27,32)(28,33)(29,34)(30,35)(31,36)(37,52)(38,53)(39,54)(40,55)(41,56)(42,62)(43,63)(44,64)(45,65)(46,66)(47,57)(48,58)(49,59)(50,60)(51,61); s4 := Sym(66)!( 7,42)( 8,46)( 9,45)(10,44)(11,43)(12,37)(13,41)(14,40)(15,39)(16,38)(17,47)(18,51)(19,50)(20,49)(21,48)(22,57)(23,61)(24,60)(25,59)(26,58)(27,52)(28,56)(29,55)(30,54)(31,53)(32,62)(33,66)(34,65)(35,64)(36,63); s5 := Sym(66)!( 7, 8)( 9,11)(12,13)(14,16)(17,18)(19,21)(22,23)(24,26)(27,28)(29,31)(32,33)(34,36)(37,38)(39,41)(42,43)(44,46)(47,48)(49,51)(52,53)(54,56)(57,58)(59,61)(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*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, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;