Polytope of Type {20,6,6} with group SmallGroup(1440,5871)

Overview

Group: SmallGroup(1440,5871)
Rank: 4
Schläfli Type: {20,6,6}
Vertices, edges, …: 20, 60, 18, 6
Order of s₀s₁s₂s₃: 30
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Universal
Non-Orientable
Flat

Quotients maximal quotients in bold

3-fold

{20,6,2}*480b

5-fold

{4,6,6}*288f

10-fold

{4,3,6}*144

15-fold

{4,6,2}*96b

30-fold

{4,3,2}*48

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := ( 1, 3)( 2, 4)( 5,19)( 6,20)( 7,17)( 8,18)( 9,15)(10,16)(11,13)(12,14)(21,23)(22,24)(25,39)(26,40)(27,37)(28,38)(29,35)(30,36)(31,33)(32,34)(41,43)(42,44)(45,59)(46,60)(47,57)(48,58)(49,55)(50,56)(51,53)(52,54);;
s1 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 9,17)(10,18)(11,20)(12,19)(15,16)(21,45)(22,46)(23,48)(24,47)(25,41)(26,42)(27,44)(28,43)(29,57)(30,58)(31,60)(32,59)(33,53)(34,54)(35,56)(36,55)(37,49)(38,50)(39,52)(40,51);;
s2 := ( 1,21)( 2,24)( 3,23)( 4,22)( 5,25)( 6,28)( 7,27)( 8,26)( 9,29)(10,32)(11,31)(12,30)(13,33)(14,36)(15,35)(16,34)(17,37)(18,40)(19,39)(20,38)(42,44)(46,48)(50,52)(54,56)(58,60);;
s3 := (21,41)(22,42)(23,43)(24,44)(25,45)(26,46)(27,47)(28,48)(29,49)(30,50)(31,51)(32,52)(33,53)(34,54)(35,55)(36,56)(37,57)(38,58)(39,59)(40,60);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2, 
s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(60)!( 1, 3)( 2, 4)( 5,19)( 6,20)( 7,17)( 8,18)( 9,15)(10,16)(11,13)(12,14)(21,23)(22,24)(25,39)(26,40)(27,37)(28,38)(29,35)(30,36)(31,33)(32,34)(41,43)(42,44)(45,59)(46,60)(47,57)(48,58)(49,55)(50,56)(51,53)(52,54);
s1 := Sym(60)!( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 9,17)(10,18)(11,20)(12,19)(15,16)(21,45)(22,46)(23,48)(24,47)(25,41)(26,42)(27,44)(28,43)(29,57)(30,58)(31,60)(32,59)(33,53)(34,54)(35,56)(36,55)(37,49)(38,50)(39,52)(40,51);
s2 := Sym(60)!( 1,21)( 2,24)( 3,23)( 4,22)( 5,25)( 6,28)( 7,27)( 8,26)( 9,29)(10,32)(11,31)(12,30)(13,33)(14,36)(15,35)(16,34)(17,37)(18,40)(19,39)(20,38)(42,44)(46,48)(50,52)(54,56)(58,60);
s3 := Sym(60)!(21,41)(22,42)(23,43)(24,44)(25,45)(26,46)(27,47)(28,48)(29,49)(30,50)(31,51)(32,52)(33,53)(34,54)(35,55)(36,56)(37,57)(38,58)(39,59)(40,60);
poly := sub<Sym(60)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2, 
s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0 >;

References