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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,12,3}*1728
if this polytope has a name.
Group : SmallGroup(1728,46116)
Rank : 5
Schlafli Type : {2,2,12,3}
Number of vertices, edges, etc : 2, 2, 72, 108, 18
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 : {2,2,12,3}*576
   4-fold quotients : {2,2,6,3}*432
   9-fold quotients : {2,2,4,3}*192
   12-fold quotients : {2,2,6,3}*144
   18-fold quotients : {2,2,4,3}*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 := ( 5, 7)( 6, 8)( 9,15)(10,16)(11,13)(12,14)(17,31)(18,32)(19,29)(20,30)
(21,39)(22,40)(23,37)(24,38)(25,35)(26,36)(27,33)(28,34);;
s3 := ( 5,17)( 6,19)( 7,18)( 8,20)( 9,21)(10,23)(11,22)(12,24)(13,25)(14,27)
(15,26)(16,28)(30,31)(34,35)(38,39);;
s4 := ( 6, 8)(10,12)(14,16)(17,33)(18,36)(19,35)(20,34)(21,37)(22,40)(23,39)
(24,38)(25,29)(26,32)(27,31)(28,30);;
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*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(40)!(1,2);
s1 := Sym(40)!(3,4);
s2 := Sym(40)!( 5, 7)( 6, 8)( 9,15)(10,16)(11,13)(12,14)(17,31)(18,32)(19,29)
(20,30)(21,39)(22,40)(23,37)(24,38)(25,35)(26,36)(27,33)(28,34);
s3 := Sym(40)!( 5,17)( 6,19)( 7,18)( 8,20)( 9,21)(10,23)(11,22)(12,24)(13,25)
(14,27)(15,26)(16,28)(30,31)(34,35)(38,39);
s4 := Sym(40)!( 6, 8)(10,12)(14,16)(17,33)(18,36)(19,35)(20,34)(21,37)(22,40)
(23,39)(24,38)(25,29)(26,32)(27,31)(28,30);
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*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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