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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,2,18}*864
if this polytope has a name.
Group : SmallGroup(864,4032)
Rank : 5
Schlafli Type : {6,2,2,18}
Number of vertices, edges, etc : 6, 6, 2, 18, 18
Order of s₀s₁s₂s₃s₄ : 18
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,2,2,18,2} of size 1728
Vertex Figure Of :
   {2,6,2,2,18} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,2,18}*432, {6,2,2,9}*432
   3-fold quotients : {2,2,2,18}*288, {6,2,2,6}*288
   4-fold quotients : {3,2,2,9}*216
   6-fold quotients : {2,2,2,9}*144, {3,2,2,6}*144, {6,2,2,3}*144
   9-fold quotients : {2,2,2,6}*96, {6,2,2,2}*96
   12-fold quotients : {3,2,2,3}*72
   18-fold quotients : {2,2,2,3}*48, {3,2,2,2}*48
   27-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,2,2,18}*1728, {6,2,2,36}*1728, {6,2,4,18}*1728a, {6,4,2,18}*1728a
Permutation Representation (GAP) :

s0 := (3,4)(5,6);;
s1 := (1,5)(2,3)(4,6);;
s2 := (7,8);;
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);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

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

Finitely Presented Group Representation (Magma) :

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

to this polytope