Polytope of Type {13,2,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {13,2,14}*728
if this polytope has a name.
Group : SmallGroup(728,36)
Rank : 4
Schlafli Type : {13,2,14}
Number of vertices, edges, etc : 13, 13, 14, 14
Order of s₀s₁s₂s₃ : 182
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {13,2,14,2} of size 1456
Vertex Figure Of :
   {2,13,2,14} of size 1456
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {13,2,7}*364
   7-fold quotients : {13,2,2}*104
Covers (Minimal Covers in Boldface) :
   2-fold covers : {13,2,28}*1456, {26,2,14}*1456
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 := (16,17)(18,19)(20,21)(22,23)(24,25)(26,27);;
s3 := (14,18)(15,16)(17,22)(19,20)(21,26)(23,24)(25,27);;
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*s0*s1*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*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(27)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13);
s1 := Sym(27)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12);
s2 := Sym(27)!(16,17)(18,19)(20,21)(22,23)(24,25)(26,27);
s3 := Sym(27)!(14,18)(15,16)(17,22)(19,20)(21,26)(23,24)(25,27);
poly := sub<Sym(27)|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*s0*s1*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*s2*s3 >;

to this polytope