Polytope of Type {31,2,2}

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

s0 := ( 2, 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);;
s1 := ( 1, 2)( 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);;
s2 := (32,33);;
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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, 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(35)!( 2, 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);
s1 := Sym(35)!( 1, 2)( 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);
s2 := Sym(35)!(32,33);
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*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, 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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