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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,3,6,3,4}*1728
if this polytope has a name.
Group : SmallGroup(1728,46116)
Rank : 7
Schlafli Type : {2,2,3,6,3,4}
Number of vertices, edges, etc : 2, 2, 3, 9, 9, 6, 4
Order of s₀s₁s₂s₃s₄s₅s₆ : 6
Order of s₀s₁s₂s₃s₄s₅s₆s₅s₄s₃s₂s₁ : 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 : {2,2,3,2,3,4}*576
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 9,13)(10,14)(11,15)(12,16)(17,29)(18,30)(19,31)(20,32)(21,37)(22,38)
(23,39)(24,40)(25,33)(26,34)(27,35)(28,36);;
s3 := ( 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);;
s4 := ( 7, 8)( 9,13)(10,14)(11,16)(12,15)(17,21)(18,22)(19,24)(20,23)(27,28)
(29,37)(30,38)(31,40)(32,39)(35,36);;
s5 := ( 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);;
s6 := ( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)
(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40);;
poly := Group([s0,s1,s2,s3,s4,s5,s6]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5","s6");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  s6 := F.7;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s6*s6, 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, 
s0*s6*s0*s6, s1*s6*s1*s6, s2*s6*s2*s6, 
s3*s6*s3*s6, s4*s6*s4*s6, s2*s3*s2*s3*s2*s3, 
s4*s5*s4*s5*s4*s5, s5*s6*s5*s6*s5*s6*s5*s6, 
s4*s6*s5*s4*s6*s5*s4*s6*s5, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, 
s5*s3*s4*s3*s4*s5*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(40)!(1,2);
s1 := Sym(40)!(3,4);
s2 := Sym(40)!( 9,13)(10,14)(11,15)(12,16)(17,29)(18,30)(19,31)(20,32)(21,37)
(22,38)(23,39)(24,40)(25,33)(26,34)(27,35)(28,36);
s3 := 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);
s4 := Sym(40)!( 7, 8)( 9,13)(10,14)(11,16)(12,15)(17,21)(18,22)(19,24)(20,23)
(27,28)(29,37)(30,38)(31,40)(32,39)(35,36);
s5 := 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);
s6 := Sym(40)!( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)
(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40);
poly := sub<Sym(40)|s0,s1,s2,s3,s4,s5,s6>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5,s6> := Group< s0,s1,s2,s3,s4,s5,s6 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s6*s6, 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, s0*s6*s0*s6, 
s1*s6*s1*s6, s2*s6*s2*s6, s3*s6*s3*s6, 
s4*s6*s4*s6, s2*s3*s2*s3*s2*s3, s4*s5*s4*s5*s4*s5, 
s5*s6*s5*s6*s5*s6*s5*s6, s4*s6*s5*s4*s6*s5*s4*s6*s5, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s5*s3*s4*s3*s4*s5*s3*s4*s3*s4 >;

to this polytope