Overview
- Group
- SmallGroup(1920,236182)
- Rank
- 6
- Schläfli Type
- {2,2,2,10,12}
- Vertices, edges, …
- 2, 2, 2, 10, 60, 12
- 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 := ( 8,11)( 9,10)(13,16)(14,15)(18,21)(19,20)(23,26)(24,25)(28,31)(29,30)(33,36)(34,35)(38,41)(39,40)(43,46)(44,45)(48,51)(49,50)(53,56)(54,55)(58,61)(59,60)(63,66)(64,65);; s4 := ( 7, 8)( 9,11)(12,18)(13,17)(14,21)(15,20)(16,19)(22,23)(24,26)(27,33)(28,32)(29,36)(30,35)(31,34)(37,53)(38,52)(39,56)(40,55)(41,54)(42,63)(43,62)(44,66)(45,65)(46,64)(47,58)(48,57)(49,61)(50,60)(51,59);; s5 := ( 7,42)( 8,43)( 9,44)(10,45)(11,46)(12,37)(13,38)(14,39)(15,40)(16,41)(17,47)(18,48)(19,49)(20,50)(21,51)(22,57)(23,58)(24,59)(25,60)(26,61)(27,52)(28,53)(29,54)(30,55)(31,56)(32,62)(33,63)(34,64)(35,65)(36,66);; 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,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(66)!(1,2); s1 := Sym(66)!(3,4); s2 := Sym(66)!(5,6); s3 := Sym(66)!( 8,11)( 9,10)(13,16)(14,15)(18,21)(19,20)(23,26)(24,25)(28,31)(29,30)(33,36)(34,35)(38,41)(39,40)(43,46)(44,45)(48,51)(49,50)(53,56)(54,55)(58,61)(59,60)(63,66)(64,65); s4 := Sym(66)!( 7, 8)( 9,11)(12,18)(13,17)(14,21)(15,20)(16,19)(22,23)(24,26)(27,33)(28,32)(29,36)(30,35)(31,34)(37,53)(38,52)(39,56)(40,55)(41,54)(42,63)(43,62)(44,66)(45,65)(46,64)(47,58)(48,57)(49,61)(50,60)(51,59); s5 := Sym(66)!( 7,42)( 8,43)( 9,44)(10,45)(11,46)(12,37)(13,38)(14,39)(15,40)(16,41)(17,47)(18,48)(19,49)(20,50)(21,51)(22,57)(23,58)(24,59)(25,60)(26,61)(27,52)(28,53)(29,54)(30,55)(31,56)(32,62)(33,63)(34,64)(35,65)(36,66); 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, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*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 >;