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Polytope of Type {2,2,2,4,18}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,4,18}*1152a
if this polytope has a name.
Group : SmallGroup(1152,153166)
Rank : 6
Schlafli Type : {2,2,2,4,18}
Number of vertices, edges, etc : 2, 2, 2, 4, 36, 18
Order of s0s1s2s3s4s5 : 36
Order of s0s1s2s3s4s5s4s3s2s1 : 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) :
   2-fold quotients : {2,2,2,2,18}*576
   3-fold quotients : {2,2,2,4,6}*384a
   4-fold quotients : {2,2,2,2,9}*288
   6-fold quotients : {2,2,2,2,6}*192
   9-fold quotients : {2,2,2,4,2}*128
   12-fold quotients : {2,2,2,2,3}*96
   18-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := (25,34)(26,35)(27,36)(28,37)(29,38)(30,39)(31,40)(32,41)(33,42);;
s4 := ( 7,25)( 8,27)( 9,26)(10,32)(11,31)(12,33)(13,29)(14,28)(15,30)(16,34)
(17,36)(18,35)(19,41)(20,40)(21,42)(22,38)(23,37)(24,39);;
s5 := ( 7,10)( 8,12)( 9,11)(13,14)(16,19)(17,21)(18,20)(22,23)(25,28)(26,30)
(27,29)(31,32)(34,37)(35,39)(36,38)(40,41);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*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, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(42)!(1,2);
s1 := Sym(42)!(3,4);
s2 := Sym(42)!(5,6);
s3 := Sym(42)!(25,34)(26,35)(27,36)(28,37)(29,38)(30,39)(31,40)(32,41)(33,42);
s4 := Sym(42)!( 7,25)( 8,27)( 9,26)(10,32)(11,31)(12,33)(13,29)(14,28)(15,30)
(16,34)(17,36)(18,35)(19,41)(20,40)(21,42)(22,38)(23,37)(24,39);
s5 := Sym(42)!( 7,10)( 8,12)( 9,11)(13,14)(16,19)(17,21)(18,20)(22,23)(25,28)
(26,30)(27,29)(31,32)(34,37)(35,39)(36,38)(40,41);
poly := sub<Sym(42)|s0,s1,s2,s3,s4,s5>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*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, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >; 
 

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