Polytope of Type {3,2,13}

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

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

to this polytope