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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,3,6,2}*1728
if this polytope has a name.
Group : SmallGroup(1728,46116)
Rank : 6
Schlafli Type : {2,4,3,6,2}
Number of vertices, edges, etc : 2, 4, 18, 27, 18, 2
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 : {2,4,3,6,2}*576
   9-fold quotients : {2,4,3,2,2}*192
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)(15,27)(16,29)(17,28)(18,30)(19,31)(20,33)(21,32)
(22,34)(23,35)(24,37)(25,36)(26,38);;
s3 := ( 3,19)( 4,22)( 5,21)( 6,20)( 7,23)( 8,26)( 9,25)(10,24)(11,15)(12,18)
(13,17)(14,16)(28,30)(32,34)(36,38);;
s4 := ( 7,11)( 8,12)( 9,13)(10,14)(15,27)(16,28)(17,29)(18,30)(19,35)(20,36)
(21,37)(22,38)(23,31)(24,32)(25,33)(26,34);;
s5 := (39,40);;
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, 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, 
s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s1*s2*s3*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

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