Polytope of Type {2,2,31}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,31}*248
if this polytope has a name.
Group : SmallGroup(248,11)
Rank : 4
Schlafli Type : {2,2,31}
Number of vertices, edges, etc : 2, 2, 31, 31
Order of s0s1s2s3 : 62
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,31,2} of size 496
Vertex Figure Of :
   {2,2,2,31} of size 496
   {3,2,2,31} of size 744
   {4,2,2,31} of size 992
   {5,2,2,31} of size 1240
   {6,2,2,31} of size 1488
   {7,2,2,31} of size 1736
   {8,2,2,31} of size 1984
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,31}*496, {2,2,62}*496
   3-fold covers : {6,2,31}*744, {2,2,93}*744
   4-fold covers : {8,2,31}*992, {2,2,124}*992, {2,4,62}*992, {4,2,62}*992
   5-fold covers : {10,2,31}*1240, {2,2,155}*1240
   6-fold covers : {12,2,31}*1488, {4,2,93}*1488, {2,6,62}*1488, {6,2,62}*1488, {2,2,186}*1488
   7-fold covers : {14,2,31}*1736, {2,2,217}*1736
   8-fold covers : {16,2,31}*1984, {4,4,62}*1984, {2,4,124}*1984, {4,2,124}*1984, {2,8,62}*1984, {8,2,62}*1984, {2,2,248}*1984
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 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);;
s3 := ( 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);;
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*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(35)!(1,2);
s1 := Sym(35)!(3,4);
s2 := Sym(35)!( 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);
s3 := Sym(35)!( 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);
poly := sub<Sym(35)|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*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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