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Polytope of Type {2,2,2,18,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,18,6}*1728a
if this polytope has a name.
Group : SmallGroup(1728,46164)
Rank : 6
Schlafli Type : {2,2,2,18,6}
Number of vertices, edges, etc : 2, 2, 2, 18, 54, 6
Order of s0s1s2s3s4s5 : 18
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) :
   3-fold quotients : {2,2,2,18,2}*576, {2,2,2,6,6}*576a
   6-fold quotients : {2,2,2,9,2}*288
   9-fold quotients : {2,2,2,2,6}*192, {2,2,2,6,2}*192
   18-fold quotients : {2,2,2,2,3}*96, {2,2,2,3,2}*96
   27-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 := ( 8, 9)(11,12)(14,15)(16,26)(17,25)(18,27)(19,29)(20,28)(21,30)(22,32)
(23,31)(24,33)(35,36)(38,39)(41,42)(43,53)(44,52)(45,54)(46,56)(47,55)(48,57)
(49,59)(50,58)(51,60);;
s4 := ( 7,16)( 8,18)( 9,17)(10,22)(11,24)(12,23)(13,19)(14,21)(15,20)(25,26)
(28,32)(29,31)(30,33)(34,43)(35,45)(36,44)(37,49)(38,51)(39,50)(40,46)(41,48)
(42,47)(52,53)(55,59)(56,58)(57,60);;
s5 := ( 7,37)( 8,38)( 9,39)(10,34)(11,35)(12,36)(13,40)(14,41)(15,42)(16,46)
(17,47)(18,48)(19,43)(20,44)(21,45)(22,49)(23,50)(24,51)(25,55)(26,56)(27,57)
(28,52)(29,53)(30,54)(31,58)(32,59)(33,60);;
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*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(60)!(1,2);
s1 := Sym(60)!(3,4);
s2 := Sym(60)!(5,6);
s3 := Sym(60)!( 8, 9)(11,12)(14,15)(16,26)(17,25)(18,27)(19,29)(20,28)(21,30)
(22,32)(23,31)(24,33)(35,36)(38,39)(41,42)(43,53)(44,52)(45,54)(46,56)(47,55)
(48,57)(49,59)(50,58)(51,60);
s4 := Sym(60)!( 7,16)( 8,18)( 9,17)(10,22)(11,24)(12,23)(13,19)(14,21)(15,20)
(25,26)(28,32)(29,31)(30,33)(34,43)(35,45)(36,44)(37,49)(38,51)(39,50)(40,46)
(41,48)(42,47)(52,53)(55,59)(56,58)(57,60);
s5 := Sym(60)!( 7,37)( 8,38)( 9,39)(10,34)(11,35)(12,36)(13,40)(14,41)(15,42)
(16,46)(17,47)(18,48)(19,43)(20,44)(21,45)(22,49)(23,50)(24,51)(25,55)(26,56)
(27,57)(28,52)(29,53)(30,54)(31,58)(32,59)(33,60);
poly := sub<Sym(60)|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*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

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