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

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

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

Permutation Representation (Magma) :

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

to this polytope