Polytope of Type {6,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,20}*240a
Also Known As : {6,20|2}. if this polytope has another name.
Group : SmallGroup(240,137)
Rank : 3
Schlafli Type : {6,20}
Number of vertices, edges, etc : 6, 60, 20
Order of s₀s₁s₂ : 60
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,20,2} of size 480
   {6,20,4} of size 960
   {6,20,6} of size 1440
   {6,20,8} of size 1920
   {6,20,8} of size 1920
   {6,20,4} of size 1920
Vertex Figure Of :
   {2,6,20} of size 480
   {3,6,20} of size 720
   {4,6,20} of size 960
   {3,6,20} of size 960
   {4,6,20} of size 960
   {6,6,20} of size 1440
   {6,6,20} of size 1440
   {6,6,20} of size 1440
   {8,6,20} of size 1920
   {4,6,20} of size 1920
   {6,6,20} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,10}*120
   3-fold quotients : {2,20}*80
   5-fold quotients : {6,4}*48a
   6-fold quotients : {2,10}*40
   10-fold quotients : {6,2}*24
   12-fold quotients : {2,5}*20
   15-fold quotients : {2,4}*16
   20-fold quotients : {3,2}*12
   30-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,40}*480, {12,20}*480
   3-fold covers : {18,20}*720a, {6,60}*720a, {6,60}*720b
   4-fold covers : {6,80}*960, {12,20}*960a, {24,20}*960a, {12,40}*960a, {24,20}*960b, {12,40}*960b, {6,20}*960e
   5-fold covers : {6,100}*1200a, {30,20}*1200a, {30,20}*1200b
   6-fold covers : {18,40}*1440, {36,20}*1440, {6,120}*1440a, {12,60}*1440a, {6,120}*1440b, {12,60}*1440b
   7-fold covers : {42,20}*1680a, {6,140}*1680a
   8-fold covers : {12,40}*1920a, {24,20}*1920a, {24,40}*1920a, {24,40}*1920b, {24,40}*1920c, {24,40}*1920d, {12,80}*1920a, {48,20}*1920a, {12,80}*1920b, {48,20}*1920b, {12,40}*1920b, {24,20}*1920b, {12,20}*1920a, {6,160}*1920, {6,40}*1920b, {6,40}*1920d, {6,20}*1920b, {12,20}*1920b, {12,20}*1920c
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
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