Polytope of Type {2,6,6,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,6,3}*1296e
if this polytope has a name.
Group : SmallGroup(1296,2985)
Rank : 5
Schlafli Type : {2,6,6,3}
Number of vertices, edges, etc : 2, 18, 54, 27, 3
Order of s₀s₁s₂s₃s₄ : 6
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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) :
   3-fold quotients : {2,6,6,3}*432a, {2,6,6,3}*432b
   6-fold quotients : {2,3,6,3}*216
   9-fold quotients : {2,2,6,3}*144, {2,6,2,3}*144
   18-fold quotients : {2,3,2,3}*72
   27-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29);;
s2 := ( 4, 5)( 6, 9)( 7,11)( 8,10)(12,14)(15,20)(16,19)(17,18)(21,22)(24,28)
(25,27)(26,29);;
s3 := ( 3,15)( 4,17)( 5,16)( 6,12)( 7,14)( 8,13)( 9,18)(10,20)(11,19)(21,24)
(22,26)(23,25)(28,29);;
s4 := ( 4, 5)( 6, 9)( 7,11)( 8,10)(12,21)(13,23)(14,22)(15,27)(16,29)(17,28)
(18,24)(19,26)(20,25);;
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*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*s3*s4, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(29)!(1,2);
s1 := Sym(29)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29);
s2 := Sym(29)!( 4, 5)( 6, 9)( 7,11)( 8,10)(12,14)(15,20)(16,19)(17,18)(21,22)
(24,28)(25,27)(26,29);
s3 := Sym(29)!( 3,15)( 4,17)( 5,16)( 6,12)( 7,14)( 8,13)( 9,18)(10,20)(11,19)
(21,24)(22,26)(23,25)(28,29);
s4 := Sym(29)!( 4, 5)( 6, 9)( 7,11)( 8,10)(12,21)(13,23)(14,22)(15,27)(16,29)
(17,28)(18,24)(19,26)(20,25);
poly := sub<Sym(29)|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*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*s3*s4, 
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2 >;

to this polytope