Polytope of Type {4,2,3,6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,3,6,6}*1728b
if this polytope has a name.
Group : SmallGroup(1728,47341)
Rank : 6
Schlafli Type : {4,2,3,6,6}
Number of vertices, edges, etc : 4, 4, 3, 9, 18, 6
Order of s₀s₁s₂s₃s₄s₅ : 12
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) :
   2-fold quotients : {2,2,3,6,6}*864b
   3-fold quotients : {4,2,3,2,6}*576, {4,2,3,6,2}*576
   6-fold quotients : {4,2,3,2,3}*288, {2,2,3,2,6}*288, {2,2,3,6,2}*288
   9-fold quotients : {4,2,3,2,2}*192
   12-fold quotients : {2,2,3,2,3}*144
   18-fold quotients : {2,2,3,2,2}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 8,11)( 9,12)(10,13)(14,23)(15,24)(16,25)(17,29)(18,30)(19,31)(20,26)
(21,27)(22,28);;
s3 := ( 5,17)( 6,18)( 7,19)( 8,14)( 9,15)(10,16)(11,20)(12,21)(13,22)(23,26)
(24,27)(25,28);;
s4 := ( 6, 7)( 9,10)(12,13)(14,23)(15,25)(16,24)(17,26)(18,28)(19,27)(20,29)
(21,31)(22,30);;
s5 := ( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30);;
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, 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*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s3*s4*s5*s4*s3*s4*s5*s4, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(31)!(2,3);
s1 := Sym(31)!(1,2)(3,4);
s2 := Sym(31)!( 8,11)( 9,12)(10,13)(14,23)(15,24)(16,25)(17,29)(18,30)(19,31)
(20,26)(21,27)(22,28);
s3 := Sym(31)!( 5,17)( 6,18)( 7,19)( 8,14)( 9,15)(10,16)(11,20)(12,21)(13,22)
(23,26)(24,27)(25,28);
s4 := Sym(31)!( 6, 7)( 9,10)(12,13)(14,23)(15,25)(16,24)(17,26)(18,28)(19,27)
(20,29)(21,31)(22,30);
s5 := Sym(31)!( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30);
poly := sub<Sym(31)|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, 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*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s5*s4*s3*s4*s5*s4, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;

to this polytope