Polytope of Type {2,6,2,18,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,2,18,2}*1728
if this polytope has a name.
Group : SmallGroup(1728,46164)
Rank : 6
Schlafli Type : {2,6,2,18,2}
Number of vertices, edges, etc : 2, 6, 6, 18, 18, 2
Order of s₀s₁s₂s₃s₄s₅ : 18
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 : {2,3,2,18,2}*864, {2,6,2,9,2}*864
   3-fold quotients : {2,2,2,18,2}*576, {2,6,2,6,2}*576
   4-fold quotients : {2,3,2,9,2}*432
   6-fold quotients : {2,2,2,9,2}*288, {2,3,2,6,2}*288, {2,6,2,3,2}*288
   9-fold quotients : {2,2,2,6,2}*192, {2,6,2,2,2}*192
   12-fold quotients : {2,3,2,3,2}*144
   18-fold quotients : {2,2,2,3,2}*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);;
s2 := (3,7)(4,5)(6,8);;
s3 := (11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26);;
s4 := ( 9,13)(10,11)(12,17)(14,15)(16,21)(18,19)(20,25)(22,23)(24,26);;
s5 := (27,28);;
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, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(28)!(1,2);
s1 := Sym(28)!(5,6)(7,8);
s2 := Sym(28)!(3,7)(4,5)(6,8);
s3 := Sym(28)!(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26);
s4 := Sym(28)!( 9,13)(10,11)(12,17)(14,15)(16,21)(18,19)(20,25)(22,23)(24,26);
s5 := Sym(28)!(27,28);
poly := sub<Sym(28)|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, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

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