Polytope of Type {13,2,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {13,2,4}*208
if this polytope has a name.
Group : SmallGroup(208,39)
Rank : 4
Schlafli Type : {13,2,4}
Number of vertices, edges, etc : 13, 13, 4, 4
Order of s₀s₁s₂s₃ : 52
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {13,2,4,2} of size 416
   {13,2,4,3} of size 624
   {13,2,4,4} of size 832
   {13,2,4,6} of size 1248
   {13,2,4,3} of size 1248
   {13,2,4,6} of size 1248
   {13,2,4,6} of size 1248
   {13,2,4,8} of size 1664
   {13,2,4,8} of size 1664
   {13,2,4,4} of size 1664
   {13,2,4,9} of size 1872
   {13,2,4,4} of size 1872
   {13,2,4,6} of size 1872
Vertex Figure Of :
   {2,13,2,4} of size 416
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {13,2,2}*104
Covers (Minimal Covers in Boldface) :
   2-fold covers : {13,2,8}*416, {26,2,4}*416
   3-fold covers : {13,2,12}*624, {39,2,4}*624
   4-fold covers : {13,2,16}*832, {52,2,4}*832, {26,4,4}*832, {26,2,8}*832
   5-fold covers : {13,2,20}*1040, {65,2,4}*1040
   6-fold covers : {13,2,24}*1248, {39,2,8}*1248, {26,2,12}*1248, {26,6,4}*1248a, {78,2,4}*1248
   7-fold covers : {13,2,28}*1456, {91,2,4}*1456
   8-fold covers : {13,2,32}*1664, {52,4,4}*1664, {26,4,8}*1664a, {26,8,4}*1664a, {26,4,8}*1664b, {26,8,4}*1664b, {26,4,4}*1664, {52,2,8}*1664, {104,2,4}*1664, {26,2,16}*1664
   9-fold covers : {13,2,36}*1872, {117,2,4}*1872, {39,2,12}*1872, {39,6,4}*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)(16,17);;
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*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(17)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13);
s1 := Sym(17)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12);
s2 := Sym(17)!(15,16);
s3 := Sym(17)!(14,15)(16,17);
poly := sub<Sym(17)|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*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