Polytope of Type {20,6} with group SmallGroup(240,137)

Overview

Group: SmallGroup(240,137)
Rank: 3
Schläfli Type: {20,6}
Vertices, edges, …: 20, 60, 6
Order of s₀s₁s₂: 60
Order of s₀s₁s₂s₁: 2
Also known as: {20,6|2}. if this polytope has another name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

2-fold

{10,6}*120

3-fold

{20,2}*80

5-fold

{4,6}*48a

6-fold

{10,2}*40

10-fold

{2,6}*24

12-fold

{5,2}*20

15-fold

{4,2}*16

20-fold

{2,3}*12

30-fold

{2,2}*8

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

7-fold

8-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

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

Finitely Presented Group Representation (GAP)

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

Permutation Representation (Magma)

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

Finitely Presented Group Representation (Magma)

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

References