Overview
- Group
- SmallGroup(1920,236184)
- Rank
- 6
- Schläfli Type
- {2,2,2,6,20}
- Vertices, edges, …
- 2, 2, 2, 6, 60, 20
- 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)(42,47)(43,48)(44,49)(45,50)(46,51)(57,62)(58,63)(59,64)(60,65)(61,66);; s4 := ( 7,12)( 8,16)( 9,15)(10,14)(11,13)(18,21)(19,20)(22,27)(23,31)(24,30)(25,29)(26,28)(33,36)(34,35)(37,57)(38,61)(39,60)(40,59)(41,58)(42,52)(43,56)(44,55)(45,54)(46,53)(47,62)(48,66)(49,65)(50,64)(51,63);; s5 := ( 7,38)( 8,37)( 9,41)(10,40)(11,39)(12,43)(13,42)(14,46)(15,45)(16,44)(17,48)(18,47)(19,51)(20,50)(21,49)(22,53)(23,52)(24,56)(25,55)(26,54)(27,58)(28,57)(29,61)(30,60)(31,59)(32,63)(33,62)(34,66)(35,65)(36,64);; 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,
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)!(12,17)(13,18)(14,19)(15,20)(16,21)(27,32)(28,33)(29,34)(30,35)(31,36)(42,47)(43,48)(44,49)(45,50)(46,51)(57,62)(58,63)(59,64)(60,65)(61,66); s4 := Sym(66)!( 7,12)( 8,16)( 9,15)(10,14)(11,13)(18,21)(19,20)(22,27)(23,31)(24,30)(25,29)(26,28)(33,36)(34,35)(37,57)(38,61)(39,60)(40,59)(41,58)(42,52)(43,56)(44,55)(45,54)(46,53)(47,62)(48,66)(49,65)(50,64)(51,63); s5 := Sym(66)!( 7,38)( 8,37)( 9,41)(10,40)(11,39)(12,43)(13,42)(14,46)(15,45)(16,44)(17,48)(18,47)(19,51)(20,50)(21,49)(22,53)(23,52)(24,56)(25,55)(26,54)(27,58)(28,57)(29,61)(30,60)(31,59)(32,63)(33,62)(34,66)(35,65)(36,64); 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, 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 >;