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Polytope of Type {62,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {62,2}*248
if this polytope has a name.
Group : SmallGroup(248,11)
Rank : 3
Schlafli Type : {62,2}
Number of vertices, edges, etc : 62, 62, 2
Order of s0s1s2 : 62
Order of s0s1s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {62,2,2} of size 496
   {62,2,3} of size 744
   {62,2,4} of size 992
   {62,2,5} of size 1240
   {62,2,6} of size 1488
   {62,2,7} of size 1736
   {62,2,8} of size 1984
Vertex Figure Of :
   {2,62,2} of size 496
   {4,62,2} of size 992
   {6,62,2} of size 1488
   {8,62,2} of size 1984
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {31,2}*124
   31-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {124,2}*496, {62,4}*496
   3-fold covers : {62,6}*744, {186,2}*744
   4-fold covers : {124,4}*992, {248,2}*992, {62,8}*992
   5-fold covers : {62,10}*1240, {310,2}*1240
   6-fold covers : {62,12}*1488, {124,6}*1488a, {372,2}*1488, {186,4}*1488a
   7-fold covers : {62,14}*1736, {434,2}*1736
   8-fold covers : {124,8}*1984a, {248,4}*1984a, {124,8}*1984b, {248,4}*1984b, {124,4}*1984, {62,16}*1984, {496,2}*1984
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)
(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)
(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(61,62);;
s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,17)(14,15)(16,21)(18,19)
(20,25)(22,23)(24,29)(26,27)(28,33)(30,31)(32,37)(34,35)(36,41)(38,39)(40,45)
(42,43)(44,49)(46,47)(48,53)(50,51)(52,57)(54,55)(56,61)(58,59)(60,62);;
s2 := (63,64);;
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, 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*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*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*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(64)!( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)
(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)
(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(61,62);
s1 := Sym(64)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,17)(14,15)(16,21)
(18,19)(20,25)(22,23)(24,29)(26,27)(28,33)(30,31)(32,37)(34,35)(36,41)(38,39)
(40,45)(42,43)(44,49)(46,47)(48,53)(50,51)(52,57)(54,55)(56,61)(58,59)(60,62);
s2 := Sym(64)!(63,64);
poly := sub<Sym(64)|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, 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*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*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*s0*s1*s0*s1 >; 
 

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