Overview
- Group
- SmallGroup(1920,236184)
- Rank
- 6
- Schläfli Type
- {2,2,20,6,2}
- Vertices, edges, …
- 2, 2, 20, 60, 6, 2
- 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 := ( 6, 9)( 7, 8)(11,14)(12,13)(16,19)(17,18)(21,24)(22,23)(26,29)(27,28)(31,34)(32,33)(35,50)(36,54)(37,53)(38,52)(39,51)(40,55)(41,59)(42,58)(43,57)(44,56)(45,60)(46,64)(47,63)(48,62)(49,61);; s3 := ( 5,36)( 6,35)( 7,39)( 8,38)( 9,37)(10,46)(11,45)(12,49)(13,48)(14,47)(15,41)(16,40)(17,44)(18,43)(19,42)(20,51)(21,50)(22,54)(23,53)(24,52)(25,61)(26,60)(27,64)(28,63)(29,62)(30,56)(31,55)(32,59)(33,58)(34,57);; s4 := ( 5,10)( 6,11)( 7,12)( 8,13)( 9,14)(20,25)(21,26)(22,27)(23,28)(24,29)(35,40)(36,41)(37,42)(38,43)(39,44)(50,55)(51,56)(52,57)(53,58)(54,59);; s5 := (65,66);; 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, 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,
s4*s5*s4*s5, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s2*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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(66)!(1,2); s1 := Sym(66)!(3,4); s2 := Sym(66)!( 6, 9)( 7, 8)(11,14)(12,13)(16,19)(17,18)(21,24)(22,23)(26,29)(27,28)(31,34)(32,33)(35,50)(36,54)(37,53)(38,52)(39,51)(40,55)(41,59)(42,58)(43,57)(44,56)(45,60)(46,64)(47,63)(48,62)(49,61); s3 := Sym(66)!( 5,36)( 6,35)( 7,39)( 8,38)( 9,37)(10,46)(11,45)(12,49)(13,48)(14,47)(15,41)(16,40)(17,44)(18,43)(19,42)(20,51)(21,50)(22,54)(23,53)(24,52)(25,61)(26,60)(27,64)(28,63)(29,62)(30,56)(31,55)(32,59)(33,58)(34,57); s4 := Sym(66)!( 5,10)( 6,11)( 7,12)( 8,13)( 9,14)(20,25)(21,26)(22,27)(23,28)(24,29)(35,40)(36,41)(37,42)(38,43)(39,44)(50,55)(51,56)(52,57)(53,58)(54,59); s5 := Sym(66)!(65,66); 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, 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, s4*s5*s4*s5, s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s2*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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;