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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,6,6,3}*1728e
if this polytope has a name.
Group : SmallGroup(1728,47874)
Rank : 6
Schlafli Type : {2,4,6,6,3}
Number of vertices, edges, etc : 2, 4, 12, 18, 9, 3
Order of s₀s₁s₂s₃s₄s₅ : 6
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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 : {2,4,6,2,3}*576c
   6-fold quotients : {2,4,3,2,3}*288
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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