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Polytope of Type {20,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,6}*240a
Also Known As : {20,6|2}. if this polytope has another name.
Group : SmallGroup(240,137)
Rank : 3
Schlafli Type : {20,6}
Number of vertices, edges, etc : 20, 60, 6
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 :
   {20,6,2} of size 480
   {20,6,3} of size 720
   {20,6,4} of size 960
   {20,6,3} of size 960
   {20,6,4} of size 960
   {20,6,6} of size 1440
   {20,6,6} of size 1440
   {20,6,6} of size 1440
   {20,6,8} of size 1920
   {20,6,4} of size 1920
   {20,6,6} of size 1920
Vertex Figure Of :
   {2,20,6} of size 480
   {4,20,6} of size 960
   {6,20,6} of size 1440
   {8,20,6} of size 1920
   {8,20,6} of size 1920
   {4,20,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,6}*120
   3-fold quotients : {20,2}*80
   5-fold quotients : {4,6}*48a
   6-fold quotients : {10,2}*40
   10-fold quotients : {2,6}*24
   12-fold quotients : {5,2}*20
   15-fold quotients : {4,2}*16
   20-fold quotients : {2,3}*12
   30-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {40,6}*480, {20,12}*480
   3-fold covers : {20,18}*720a, {60,6}*720a, {60,6}*720b
   4-fold covers : {80,6}*960, {20,12}*960a, {20,24}*960a, {40,12}*960a, {20,24}*960b, {40,12}*960b, {20,6}*960e
   5-fold covers : {100,6}*1200a, {20,30}*1200a, {20,30}*1200b
   6-fold covers : {40,18}*1440, {20,36}*1440, {120,6}*1440a, {60,12}*1440a, {120,6}*1440b, {60,12}*1440b
   7-fold covers : {20,42}*1680a, {140,6}*1680a
   8-fold covers : {40,12}*1920a, {20,24}*1920a, {40,24}*1920a, {40,24}*1920b, {40,24}*1920c, {40,24}*1920d, {80,12}*1920a, {20,48}*1920a, {80,12}*1920b, {20,48}*1920b, {40,12}*1920b, {20,24}*1920b, {20,12}*1920a, {160,6}*1920, {40,6}*1920b, {40,6}*1920d, {20,6}*1920b, {20,12}*1920b, {20,12}*1920c
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 : None.
to this polytope