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

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

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

Permutation Representation (Magma) :

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

to this polytope