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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6,4,2}*1728i
if this polytope has a name.
Group : SmallGroup(1728,47874)
Rank : 5
Schlafli Type : {6,6,4,2}
Number of vertices, edges, etc : 18, 54, 36, 4, 2
Order of s₀s₁s₂s₃s₄ : 6
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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 : {6,6,4,2}*576d, {6,6,4,2}*576e
   6-fold quotients : {6,3,4,2}*288
   9-fold quotients : {2,6,4,2}*192c
   18-fold quotients : {2,3,4,2}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, 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, 
s2*s3*s2*s3*s2*s3*s2*s3, s3*s2*s1*s3*s2*s3*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, 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, s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s2*s1*s3*s2*s3*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1 >;

to this polytope