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Polytope of Type {20,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,6,2}*480a
if this polytope has a name.
Group : SmallGroup(480,1088)
Rank : 4
Schlafli Type : {20,6,2}
Number of vertices, edges, etc : 20, 60, 6, 2
Order of s0s1s2s3 : 60
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {20,6,2,2} of size 960
   {20,6,2,3} of size 1440
   {20,6,2,4} of size 1920
Vertex Figure Of :
   {2,20,6,2} of size 960
   {4,20,6,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,6,2}*240
   3-fold quotients : {20,2,2}*160
   5-fold quotients : {4,6,2}*96a
   6-fold quotients : {10,2,2}*80
   10-fold quotients : {2,6,2}*48
   12-fold quotients : {5,2,2}*40
   15-fold quotients : {4,2,2}*32
   20-fold quotients : {2,3,2}*24
   30-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {20,6,4}*960a, {40,6,2}*960, {20,12,2}*960
   3-fold covers : {20,18,2}*1440a, {20,6,6}*1440a, {20,6,6}*1440b, {60,6,2}*1440a, {60,6,2}*1440b
   4-fold covers : {20,12,4}*1920a, {40,12,2}*1920a, {20,24,2}*1920a, {40,12,2}*1920b, {20,24,2}*1920b, {20,12,2}*1920a, {20,6,8}*1920, {40,6,4}*1920a, {80,6,2}*1920, {20,6,4}*1920a, {20,6,2}*1920a
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);;
s3 := (61,62);;
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, s2*s3*s2*s3, 
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(62)!( 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(62)!( 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(62)!( 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);
s3 := Sym(62)!(61,62);
poly := sub<Sym(62)|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, 
s2*s3*s2*s3, 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 >; 
 

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