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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,3,6}*1728
if this polytope has a name.
Group : SmallGroup(1728,46116)
Rank : 5
Schlafli Type : {2,2,3,6}
Number of vertices, edges, etc : 2, 2, 36, 108, 72
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   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 : {2,2,3,6}*576
   4-fold quotients : {2,2,3,6}*432
   9-fold quotients : {2,2,3,6}*192
   12-fold quotients : {2,2,3,6}*144
   18-fold quotients : {2,2,3,3}*96
   36-fold quotients : {2,2,3,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

to this polytope