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

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

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

Permutation Representation (Magma) :

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

to this polytope