Polytope of Type {6,2,13}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,13}*312
if this polytope has a name.
Group : SmallGroup(312,54)
Rank : 4
Schlafli Type : {6,2,13}
Number of vertices, edges, etc : 6, 6, 13, 13
Order of s₀s₁s₂s₃ : 78
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,2,13,2} of size 624
Vertex Figure Of :
   {2,6,2,13} of size 624
   {3,6,2,13} of size 936
   {4,6,2,13} of size 1248
   {3,6,2,13} of size 1248
   {4,6,2,13} of size 1248
   {4,6,2,13} of size 1248
   {4,6,2,13} of size 1872
   {6,6,2,13} of size 1872
   {6,6,2,13} of size 1872
   {6,6,2,13} of size 1872
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,13}*156
   3-fold quotients : {2,2,13}*104
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,2,13}*624, {6,2,26}*624
   3-fold covers : {18,2,13}*936, {6,2,39}*936
   4-fold covers : {24,2,13}*1248, {12,2,26}*1248, {6,2,52}*1248, {6,4,26}*1248
   5-fold covers : {30,2,13}*1560, {6,2,65}*1560
   6-fold covers : {36,2,13}*1872, {18,2,26}*1872, {12,2,39}*1872, {6,6,26}*1872a, {6,6,26}*1872c, {6,2,78}*1872
Permutation Representation (GAP) :

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

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