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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {13,2,2,2}*208
if this polytope has a name.
Group : SmallGroup(208,50)
Rank : 5
Schlafli Type : {13,2,2,2}
Number of vertices, edges, etc : 13, 13, 2, 2, 2
Order of s₀s₁s₂s₃s₄ : 26
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {13,2,2,2,2} of size 416
   {13,2,2,2,3} of size 624
   {13,2,2,2,4} of size 832
   {13,2,2,2,5} of size 1040
   {13,2,2,2,6} of size 1248
   {13,2,2,2,7} of size 1456
   {13,2,2,2,8} of size 1664
   {13,2,2,2,9} of size 1872
Vertex Figure Of :
   {2,13,2,2,2} of size 416
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {13,2,2,4}*416, {13,2,4,2}*416, {26,2,2,2}*416
   3-fold covers : {13,2,2,6}*624, {13,2,6,2}*624, {39,2,2,2}*624
   4-fold covers : {13,2,4,4}*832, {13,2,2,8}*832, {13,2,8,2}*832, {52,2,2,2}*832, {26,2,2,4}*832, {26,2,4,2}*832, {26,4,2,2}*832
   5-fold covers : {13,2,2,10}*1040, {13,2,10,2}*1040, {65,2,2,2}*1040
   6-fold covers : {13,2,2,12}*1248, {13,2,12,2}*1248, {13,2,4,6}*1248a, {13,2,6,4}*1248a, {39,2,2,4}*1248, {39,2,4,2}*1248, {26,2,2,6}*1248, {26,2,6,2}*1248, {26,6,2,2}*1248, {78,2,2,2}*1248
   7-fold covers : {13,2,2,14}*1456, {13,2,14,2}*1456, {91,2,2,2}*1456
   8-fold covers : {13,2,4,8}*1664a, {13,2,8,4}*1664a, {13,2,4,8}*1664b, {13,2,8,4}*1664b, {13,2,4,4}*1664, {13,2,2,16}*1664, {13,2,16,2}*1664, {26,2,4,4}*1664, {26,4,4,2}*1664, {52,4,2,2}*1664, {26,4,2,4}*1664, {52,2,2,4}*1664, {52,2,4,2}*1664, {26,2,2,8}*1664, {26,2,8,2}*1664, {26,8,2,2}*1664, {104,2,2,2}*1664
   9-fold covers : {13,2,2,18}*1872, {13,2,18,2}*1872, {117,2,2,2}*1872, {13,2,6,6}*1872a, {13,2,6,6}*1872b, {13,2,6,6}*1872c, {39,2,2,6}*1872, {39,2,6,2}*1872, {39,6,2,2}*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 := (14,15);;
s3 := (16,17);;
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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, 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(19)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13);
s1 := Sym(19)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12);
s2 := Sym(19)!(14,15);
s3 := Sym(19)!(16,17);
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*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, 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