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Polytope of Type {3,12,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,12,2,2}*1728
if this polytope has a name.
Group : SmallGroup(1728,46116)
Rank : 5
Schlafli Type : {3,12,2,2}
Number of vertices, edges, etc : 18, 108, 72, 2, 2
Order of s0s1s2s3s4 : 6
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 : {3,12,2,2}*576
   4-fold quotients : {3,6,2,2}*432
   9-fold quotients : {3,4,2,2}*192
   12-fold quotients : {3,6,2,2}*144
   18-fold quotients : {3,4,2,2}*96
   36-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 3)( 6, 7)(10,11)(13,25)(14,27)(15,26)(16,28)(17,29)(18,31)(19,30)
(20,32)(21,33)(22,35)(23,34)(24,36);;
s1 := ( 1,17)( 2,20)( 3,19)( 4,18)( 5,21)( 6,24)( 7,23)( 8,22)( 9,13)(10,16)
(11,15)(12,14)(26,28)(30,32)(34,36);;
s2 := ( 1, 4)( 2, 3)( 5,12)( 6,11)( 7,10)( 8, 9)(13,28)(14,27)(15,26)(16,25)
(17,36)(18,35)(19,34)(20,33)(21,32)(22,31)(23,30)(24,29);;
s3 := (37,38);;
s4 := (39,40);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(40)!( 2, 3)( 6, 7)(10,11)(13,25)(14,27)(15,26)(16,28)(17,29)(18,31)
(19,30)(20,32)(21,33)(22,35)(23,34)(24,36);
s1 := Sym(40)!( 1,17)( 2,20)( 3,19)( 4,18)( 5,21)( 6,24)( 7,23)( 8,22)( 9,13)
(10,16)(11,15)(12,14)(26,28)(30,32)(34,36);
s2 := Sym(40)!( 1, 4)( 2, 3)( 5,12)( 6,11)( 7,10)( 8, 9)(13,28)(14,27)(15,26)
(16,25)(17,36)(18,35)(19,34)(20,33)(21,32)(22,31)(23,30)(24,29);
s3 := Sym(40)!(37,38);
s4 := Sym(40)!(39,40);
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*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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