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

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

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