Polytope of Type {2,6,6,2,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,6,2,6}*1728c
if this polytope has a name.
Group : SmallGroup(1728,47915)
Rank : 6
Schlafli Type : {2,6,6,2,6}
Number of vertices, edges, etc : 2, 6, 18, 6, 6, 6
Order of s₀s₁s₂s₃s₄s₅ : 6
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,3,6,2,6}*864, {2,6,6,2,3}*864c
   3-fold quotients : {2,6,2,2,6}*576, {2,6,6,2,2}*576c
   4-fold quotients : {2,3,6,2,3}*432
   6-fold quotients : {2,3,2,2,6}*288, {2,3,6,2,2}*288, {2,6,2,2,3}*288
   9-fold quotients : {2,2,2,2,6}*192, {2,6,2,2,2}*192
   12-fold quotients : {2,3,2,2,3}*144
   18-fold quotients : {2,2,2,2,3}*96, {2,3,2,2,2}*96
   27-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 5, 6)( 7, 8)( 9,10)(11,12)(13,16)(14,15)(17,20)(18,19);;
s2 := ( 3,17)( 4,13)( 5,11)( 6,19)( 7, 9)( 8,18)(10,15)(12,14)(16,20);;
s3 := ( 7, 8)(11,12)(13,14)(15,16)(17,18)(19,20);;
s4 := (23,24)(25,26);;
s5 := (21,25)(22,23)(24,26);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(26)!(1,2);
s1 := Sym(26)!( 5, 6)( 7, 8)( 9,10)(11,12)(13,16)(14,15)(17,20)(18,19);
s2 := Sym(26)!( 3,17)( 4,13)( 5,11)( 6,19)( 7, 9)( 8,18)(10,15)(12,14)(16,20);
s3 := Sym(26)!( 7, 8)(11,12)(13,14)(15,16)(17,18)(19,20);
s4 := Sym(26)!(23,24)(25,26);
s5 := Sym(26)!(21,25)(22,23)(24,26);
poly := sub<Sym(26)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;

to this polytope