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

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

s0 := (2,3);;
s1 := (1,2);;
s2 := (22,31)(23,32)(24,33)(25,34)(26,35)(27,36)(28,37)(29,38)(30,39);;
s3 := ( 4,22)( 5,23)( 6,24)( 7,28)( 8,29)( 9,30)(10,25)(11,26)(12,27)(13,31)
(14,32)(15,33)(16,37)(17,38)(18,39)(19,34)(20,35)(21,36);;
s4 := ( 4, 7)( 5, 9)( 6, 8)(11,12)(13,16)(14,18)(15,17)(20,21)(22,25)(23,27)
(24,26)(29,30)(31,34)(32,36)(33,35)(38,39);;
s5 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)
(34,35)(37,38);;
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, s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s5*s4*s3*s4*s5*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(39)!(2,3);
s1 := Sym(39)!(1,2);
s2 := Sym(39)!(22,31)(23,32)(24,33)(25,34)(26,35)(27,36)(28,37)(29,38)(30,39);
s3 := Sym(39)!( 4,22)( 5,23)( 6,24)( 7,28)( 8,29)( 9,30)(10,25)(11,26)(12,27)
(13,31)(14,32)(15,33)(16,37)(17,38)(18,39)(19,34)(20,35)(21,36);
s4 := Sym(39)!( 4, 7)( 5, 9)( 6, 8)(11,12)(13,16)(14,18)(15,17)(20,21)(22,25)
(23,27)(24,26)(29,30)(31,34)(32,36)(33,35)(38,39);
s5 := Sym(39)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)
(31,32)(34,35)(37,38);
poly := sub<Sym(39)|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, 
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s5*s4*s3*s4*s5*s4, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;

to this polytope