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

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

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

Permutation Representation (Magma) :

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

to this polytope