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

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

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

Permutation Representation (Magma) :

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

to this polytope