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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,6,2,3}*1728b
if this polytope has a name.
Group : SmallGroup(1728,47341)
Rank : 6
Schlafli Type : {4,6,6,2,3}
Number of vertices, edges, etc : 4, 12, 18, 6, 3, 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 : {2,6,6,2,3}*864c
   3-fold quotients : {4,6,2,2,3}*576a
   4-fold quotients : {2,3,6,2,3}*432
   6-fold quotients : {2,6,2,2,3}*288
   9-fold quotients : {4,2,2,2,3}*192
   12-fold quotients : {2,3,2,2,3}*144
   18-fold quotients : {2,2,2,2,3}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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