Polytope of Type {3,2,18,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,18,6}*1296b
if this polytope has a name.
Group : SmallGroup(1296,2984)
Rank : 5
Schlafli Type : {3,2,18,6}
Number of vertices, edges, etc : 3, 3, 18, 54, 6
Order of s0s1s2s3s4 : 18
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) :
   2-fold quotients : {3,2,9,6}*648
   3-fold quotients : {3,2,18,2}*432, {3,2,6,6}*432c
   6-fold quotients : {3,2,9,2}*216, {3,2,3,6}*216
   9-fold quotients : {3,2,6,2}*144
   18-fold quotients : {3,2,3,2}*72
   27-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 5, 6)( 7,10)( 8,12)( 9,11)(13,23)(14,22)(15,24)(16,29)(17,28)(18,30)
(19,26)(20,25)(21,27)(32,33)(34,37)(35,39)(36,38)(40,50)(41,49)(42,51)(43,56)
(44,55)(45,57)(46,53)(47,52)(48,54);;
s3 := ( 4,43)( 5,45)( 6,44)( 7,40)( 8,42)( 9,41)(10,46)(11,48)(12,47)(13,34)
(14,36)(15,35)(16,31)(17,33)(18,32)(19,37)(20,39)(21,38)(22,53)(23,52)(24,54)
(25,50)(26,49)(27,51)(28,56)(29,55)(30,57);;
s4 := ( 7,10)( 8,11)( 9,12)(16,19)(17,20)(18,21)(25,28)(26,29)(27,30)(34,37)
(35,38)(36,39)(43,46)(44,47)(45,48)(52,55)(53,56)(54,57);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, 
s2*s3*s4*s3*s2*s3*s2*s3*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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(57)!(2,3);
s1 := Sym(57)!(1,2);
s2 := Sym(57)!( 5, 6)( 7,10)( 8,12)( 9,11)(13,23)(14,22)(15,24)(16,29)(17,28)
(18,30)(19,26)(20,25)(21,27)(32,33)(34,37)(35,39)(36,38)(40,50)(41,49)(42,51)
(43,56)(44,55)(45,57)(46,53)(47,52)(48,54);
s3 := Sym(57)!( 4,43)( 5,45)( 6,44)( 7,40)( 8,42)( 9,41)(10,46)(11,48)(12,47)
(13,34)(14,36)(15,35)(16,31)(17,33)(18,32)(19,37)(20,39)(21,38)(22,53)(23,52)
(24,54)(25,50)(26,49)(27,51)(28,56)(29,55)(30,57);
s4 := Sym(57)!( 7,10)( 8,11)( 9,12)(16,19)(17,20)(18,21)(25,28)(26,29)(27,30)
(34,37)(35,38)(36,39)(43,46)(44,47)(45,48)(52,55)(53,56)(54,57);
poly := sub<Sym(57)|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, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s2*s3*s4*s3*s2*s3*s2*s3*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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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