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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,6,6}*1296d
if this polytope has a name.
Group : SmallGroup(1296,3538)
Rank : 5
Schlafli Type : {3,2,6,6}
Number of vertices, edges, etc : 3, 3, 18, 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 : {3,2,6,6}*432a, {3,2,6,6}*432b, {3,2,6,6}*432c
   6-fold quotients : {3,2,3,6}*216, {3,2,6,3}*216
   9-fold quotients : {3,2,2,6}*144, {3,2,6,2}*144
   18-fold quotients : {3,2,2,3}*72, {3,2,3,2}*72
   27-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := ( 7,10)( 8,11)( 9,12)(13,22)(14,23)(15,24)(16,28)(17,29)(18,30)(19,25)
(20,26)(21,27);;
s3 := ( 4,16)( 5,18)( 6,17)( 7,13)( 8,15)( 9,14)(10,19)(11,21)(12,20)(22,25)
(23,27)(24,26)(29,30);;
s4 := ( 4, 5)( 7, 8)(10,11)(13,23)(14,22)(15,24)(16,26)(17,25)(18,27)(19,29)
(20,28)(21,30);;
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, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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(30)!(2,3);
s1 := Sym(30)!(1,2);
s2 := Sym(30)!( 7,10)( 8,11)( 9,12)(13,22)(14,23)(15,24)(16,28)(17,29)(18,30)
(19,25)(20,26)(21,27);
s3 := Sym(30)!( 4,16)( 5,18)( 6,17)( 7,13)( 8,15)( 9,14)(10,19)(11,21)(12,20)
(22,25)(23,27)(24,26)(29,30);
s4 := Sym(30)!( 4, 5)( 7, 8)(10,11)(13,23)(14,22)(15,24)(16,26)(17,25)(18,27)
(19,29)(20,28)(21,30);
poly := sub<Sym(30)|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, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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