Polytope of Type {13,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {13,2,3}*156
if this polytope has a name.
Group : SmallGroup(156,11)
Rank : 4
Schlafli Type : {13,2,3}
Number of vertices, edges, etc : 13, 13, 3, 3
Order of s₀s₁s₂s₃ : 39
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {13,2,3,2} of size 312
   {13,2,3,3} of size 624
   {13,2,3,4} of size 624
   {13,2,3,6} of size 936
   {13,2,3,4} of size 1248
   {13,2,3,6} of size 1248
   {13,2,3,5} of size 1560
Vertex Figure Of :
   {2,13,2,3} of size 312
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {13,2,6}*312, {26,2,3}*312
   3-fold covers : {13,2,9}*468, {39,2,3}*468
   4-fold covers : {13,2,12}*624, {52,2,3}*624, {26,2,6}*624
   5-fold covers : {13,2,15}*780, {65,2,3}*780
   6-fold covers : {13,2,18}*936, {26,2,9}*936, {26,6,3}*936, {39,2,6}*936, {78,2,3}*936
   7-fold covers : {13,2,21}*1092, {91,2,3}*1092
   8-fold covers : {13,2,24}*1248, {104,2,3}*1248, {26,2,12}*1248, {52,2,6}*1248, {26,4,6}*1248, {26,4,3}*1248
   9-fold covers : {13,2,27}*1404, {117,2,3}*1404, {39,2,9}*1404, {39,6,3}*1404
   10-fold covers : {13,2,30}*1560, {26,2,15}*1560, {65,2,6}*1560, {130,2,3}*1560
   11-fold covers : {13,2,33}*1716, {143,2,3}*1716
   12-fold covers : {13,2,36}*1872, {52,2,9}*1872, {26,2,18}*1872, {52,6,3}*1872, {39,2,12}*1872, {156,2,3}*1872, {26,6,6}*1872a, {26,6,6}*1872b, {78,2,6}*1872
Permutation Representation (GAP) :

s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12);;
s2 := (15,16);;
s3 := (14,15);;
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*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(16)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13);
s1 := Sym(16)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12);
s2 := Sym(16)!(15,16);
s3 := Sym(16)!(14,15);
poly := sub<Sym(16)|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*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 >;

to this polytope