Polytope of Type {2,2,13,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,13,2}*208
if this polytope has a name.
Group : SmallGroup(208,50)
Rank : 5
Schlafli Type : {2,2,13,2}
Number of vertices, edges, etc : 2, 2, 13, 13, 2
Order of s₀s₁s₂s₃s₄ : 26
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,13,2,2} of size 416
   {2,2,13,2,3} of size 624
   {2,2,13,2,4} of size 832
   {2,2,13,2,5} of size 1040
   {2,2,13,2,6} of size 1248
   {2,2,13,2,7} of size 1456
   {2,2,13,2,8} of size 1664
   {2,2,13,2,9} of size 1872
Vertex Figure Of :
   {2,2,2,13,2} of size 416
   {3,2,2,13,2} of size 624
   {4,2,2,13,2} of size 832
   {5,2,2,13,2} of size 1040
   {6,2,2,13,2} of size 1248
   {7,2,2,13,2} of size 1456
   {8,2,2,13,2} of size 1664
   {9,2,2,13,2} of size 1872
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,13,2}*416, {2,2,26,2}*416
   3-fold covers : {6,2,13,2}*624, {2,2,39,2}*624
   4-fold covers : {8,2,13,2}*832, {2,2,52,2}*832, {2,2,26,4}*832, {2,4,26,2}*832, {4,2,26,2}*832
   5-fold covers : {10,2,13,2}*1040, {2,2,65,2}*1040
   6-fold covers : {12,2,13,2}*1248, {4,2,39,2}*1248, {2,2,26,6}*1248, {2,6,26,2}*1248, {6,2,26,2}*1248, {2,2,78,2}*1248
   7-fold covers : {14,2,13,2}*1456, {2,2,91,2}*1456
   8-fold covers : {16,2,13,2}*1664, {4,4,26,2}*1664, {2,2,52,4}*1664, {2,4,52,2}*1664, {4,2,26,4}*1664, {2,4,26,4}*1664, {4,2,52,2}*1664, {2,2,26,8}*1664, {2,8,26,2}*1664, {8,2,26,2}*1664, {2,2,104,2}*1664
   9-fold covers : {18,2,13,2}*1872, {2,2,117,2}*1872, {2,2,39,6}*1872, {2,6,39,2}*1872, {6,2,39,2}*1872
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17);;
s3 := ( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);;
s4 := (18,19);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, 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(19)!(1,2);
s1 := Sym(19)!(3,4);
s2 := Sym(19)!( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17);
s3 := Sym(19)!( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);
s4 := Sym(19)!(18,19);
poly := sub<Sym(19)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, 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