Polytope of Type {2,2,13}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,13}*104
if this polytope has a name.
Group : SmallGroup(104,13)
Rank : 4
Schlafli Type : {2,2,13}
Number of vertices, edges, etc : 2, 2, 13, 13
Order of s₀s₁s₂s₃ : 26
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,13,2} of size 208
Vertex Figure Of :
   {2,2,2,13} of size 208
   {3,2,2,13} of size 312
   {4,2,2,13} of size 416
   {5,2,2,13} of size 520
   {6,2,2,13} of size 624
   {7,2,2,13} of size 728
   {8,2,2,13} of size 832
   {9,2,2,13} of size 936
   {10,2,2,13} of size 1040
   {11,2,2,13} of size 1144
   {12,2,2,13} of size 1248
   {13,2,2,13} of size 1352
   {14,2,2,13} of size 1456
   {15,2,2,13} of size 1560
   {16,2,2,13} of size 1664
   {17,2,2,13} of size 1768
   {18,2,2,13} of size 1872
   {19,2,2,13} of size 1976
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,13}*208, {2,2,26}*208
   3-fold covers : {6,2,13}*312, {2,2,39}*312
   4-fold covers : {8,2,13}*416, {2,2,52}*416, {2,4,26}*416, {4,2,26}*416
   5-fold covers : {10,2,13}*520, {2,2,65}*520
   6-fold covers : {12,2,13}*624, {4,2,39}*624, {2,6,26}*624, {6,2,26}*624, {2,2,78}*624
   7-fold covers : {14,2,13}*728, {2,2,91}*728
   8-fold covers : {16,2,13}*832, {2,4,52}*832, {4,2,52}*832, {4,4,26}*832, {2,2,104}*832, {2,8,26}*832, {8,2,26}*832
   9-fold covers : {18,2,13}*936, {2,2,117}*936, {2,6,39}*936, {6,2,39}*936
   10-fold covers : {20,2,13}*1040, {4,2,65}*1040, {2,10,26}*1040, {10,2,26}*1040, {2,2,130}*1040
   11-fold covers : {22,2,13}*1144, {2,2,143}*1144
   12-fold covers : {24,2,13}*1248, {8,2,39}*1248, {2,12,26}*1248, {12,2,26}*1248, {2,6,52}*1248a, {6,2,52}*1248, {4,6,26}*1248a, {6,4,26}*1248, {2,2,156}*1248, {2,4,78}*1248a, {4,2,78}*1248, {2,6,39}*1248, {2,4,39}*1248
   13-fold covers : {2,2,169}*1352, {2,26,13}*1352, {26,2,13}*1352
   14-fold covers : {28,2,13}*1456, {4,2,91}*1456, {2,14,26}*1456, {14,2,26}*1456, {2,2,182}*1456
   15-fold covers : {30,2,13}*1560, {10,2,39}*1560, {6,2,65}*1560, {2,2,195}*1560
   16-fold covers : {32,2,13}*1664, {4,4,52}*1664, {4,8,26}*1664a, {8,4,26}*1664a, {2,8,52}*1664a, {2,4,104}*1664a, {4,8,26}*1664b, {8,4,26}*1664b, {2,8,52}*1664b, {2,4,104}*1664b, {4,4,26}*1664, {2,4,52}*1664, {8,2,52}*1664, {4,2,104}*1664, {2,16,26}*1664, {16,2,26}*1664, {2,2,208}*1664
   17-fold covers : {34,2,13}*1768, {2,2,221}*1768
   18-fold covers : {36,2,13}*1872, {4,2,117}*1872, {2,18,26}*1872, {18,2,26}*1872, {2,2,234}*1872, {12,2,39}*1872, {4,6,39}*1872, {6,6,26}*1872a, {6,6,26}*1872b, {6,6,26}*1872c, {2,6,78}*1872a, {2,6,78}*1872b, {2,6,78}*1872c, {6,2,78}*1872
   19-fold covers : {38,2,13}*1976, {2,2,247}*1976
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);;
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*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*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*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(17)!(1,2);
s1 := Sym(17)!(3,4);
s2 := Sym(17)!( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17);
s3 := Sym(17)!( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);
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*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*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*s2*s3 >;

to this polytope