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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,6,6}*1728
if this polytope has a name.
Group : SmallGroup(1728,46116)
Rank : 6
Schlafli Type : {2,2,4,6,6}
Number of vertices, edges, etc : 2, 2, 4, 18, 27, 9
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) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(17,19)(18,20)(21,23)(22,24)
(25,27)(26,28)(29,31)(30,32)(33,35)(34,36)(37,39)(38,40);;
s3 := ( 6, 7)( 9,13)(10,15)(11,14)(12,16)(18,19)(21,25)(22,27)(23,26)(24,28)
(30,31)(33,37)(34,39)(35,38)(36,40);;
s4 := ( 6, 8)(10,12)(14,16)(17,33)(18,36)(19,35)(20,34)(21,37)(22,40)(23,39)
(24,38)(25,29)(26,32)(27,31)(28,30);;
s5 := ( 5,17)( 6,18)( 7,19)( 8,20)( 9,25)(10,26)(11,27)(12,28)(13,21)(14,22)
(15,23)(16,24)(33,37)(34,38)(35,39)(36,40);;
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, 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, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s2*s3, 
s3*s4*s5*s3*s4*s5*s3*s4*s5, 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(40)!(1,2);
s1 := Sym(40)!(3,4);
s2 := Sym(40)!( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(17,19)(18,20)(21,23)
(22,24)(25,27)(26,28)(29,31)(30,32)(33,35)(34,36)(37,39)(38,40);
s3 := Sym(40)!( 6, 7)( 9,13)(10,15)(11,14)(12,16)(18,19)(21,25)(22,27)(23,26)
(24,28)(30,31)(33,37)(34,39)(35,38)(36,40);
s4 := Sym(40)!( 6, 8)(10,12)(14,16)(17,33)(18,36)(19,35)(20,34)(21,37)(22,40)
(23,39)(24,38)(25,29)(26,32)(27,31)(28,30);
s5 := Sym(40)!( 5,17)( 6,18)( 7,19)( 8,20)( 9,25)(10,26)(11,27)(12,28)(13,21)
(14,22)(15,23)(16,24)(33,37)(34,38)(35,39)(36,40);
poly := sub<Sym(40)|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, 
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, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s2*s3, s3*s4*s5*s3*s4*s5*s3*s4*s5, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;

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