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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6,3,6,2}*1296
if this polytope has a name.
Group : SmallGroup(1296,2985)
Rank : 6
Schlafli Type : {3,6,3,6,2}
Number of vertices, edges, etc : 3, 9, 9, 9, 6, 2
Order of s₀s₁s₂s₃s₄s₅ : 6
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) :
   3-fold quotients : {3,6,3,2,2}*432, {3,2,3,6,2}*432
   9-fold quotients : {3,2,3,2,2}*144
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27);;
s1 := ( 2, 3)( 5, 6)( 8, 9)(10,12)(13,15)(16,18)(19,20)(22,23)(25,26);;
s2 := ( 1,10)( 2,12)( 3,11)( 4,16)( 5,18)( 6,17)( 7,13)( 8,15)( 9,14)(20,21)
(22,25)(23,27)(24,26);;
s3 := ( 1, 4)( 2, 6)( 3, 5)( 8, 9)(10,22)(11,24)(12,23)(13,19)(14,21)(15,20)
(16,25)(17,27)(18,26);;
s4 := ( 4, 7)( 5, 8)( 6, 9)(13,16)(14,17)(15,18)(22,25)(23,26)(24,27);;
s5 := (28,29);;
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*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, s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(29)!( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27);
s1 := Sym(29)!( 2, 3)( 5, 6)( 8, 9)(10,12)(13,15)(16,18)(19,20)(22,23)(25,26);
s2 := Sym(29)!( 1,10)( 2,12)( 3,11)( 4,16)( 5,18)( 6,17)( 7,13)( 8,15)( 9,14)
(20,21)(22,25)(23,27)(24,26);
s3 := Sym(29)!( 1, 4)( 2, 6)( 3, 5)( 8, 9)(10,22)(11,24)(12,23)(13,19)(14,21)
(15,20)(16,25)(17,27)(18,26);
s4 := Sym(29)!( 4, 7)( 5, 8)( 6, 9)(13,16)(14,17)(15,18)(22,25)(23,26)(24,27);
s5 := Sym(29)!(28,29);
poly := sub<Sym(29)|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*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*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, 
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3 >;

to this polytope