Polytope of Type {2,31,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,31,2}*248
if this polytope has a name.
Group : SmallGroup(248,11)
Rank : 4
Schlafli Type : {2,31,2}
Number of vertices, edges, etc : 2, 31, 31, 2
Order of s₀s₁s₂s₃ : 62
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,31,2,2} of size 496
   {2,31,2,3} of size 744
   {2,31,2,4} of size 992
   {2,31,2,5} of size 1240
   {2,31,2,6} of size 1488
   {2,31,2,7} of size 1736
   {2,31,2,8} of size 1984
Vertex Figure Of :
   {2,2,31,2} of size 496
   {3,2,31,2} of size 744
   {4,2,31,2} of size 992
   {5,2,31,2} of size 1240
   {6,2,31,2} of size 1488
   {7,2,31,2} of size 1736
   {8,2,31,2} of size 1984
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,62,2}*496
   3-fold covers : {2,93,2}*744
   4-fold covers : {2,124,2}*992, {2,62,4}*992, {4,62,2}*992
   5-fold covers : {2,155,2}*1240
   6-fold covers : {2,62,6}*1488, {6,62,2}*1488, {2,186,2}*1488
   7-fold covers : {2,217,2}*1736
   8-fold covers : {2,124,4}*1984, {4,124,2}*1984, {4,62,4}*1984, {2,62,8}*1984, {8,62,2}*1984, {2,248,2}*1984
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 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);;
s2 := ( 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);;
s3 := (34,35);;
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, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, 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*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(35)!(1,2);
s1 := Sym(35)!( 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);
s2 := Sym(35)!( 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);
s3 := Sym(35)!(34,35);
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, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, 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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

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