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Polytope of Type {6,36,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,36,2}*864c
if this polytope has a name.
Group : SmallGroup(864,3998)
Rank : 4
Schlafli Type : {6,36,2}
Number of vertices, edges, etc : 6, 108, 36, 2
Order of s0s1s2s3 : 18
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,36,2,2} of size 1728
Vertex Figure Of :
   {2,6,36,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {6,12,2}*288d
   9-fold quotients : {6,4,2}*96b
   18-fold quotients : {3,4,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,36,2}*1728
Permutation Representation (GAP) :
s0 := ( 2, 3)( 6, 7)(10,11)(14,15)(18,19)(22,23)(26,27)(30,31)(34,35);;
s1 := ( 3, 4)( 5, 9)( 6,10)( 7,12)( 8,11)(13,29)(14,30)(15,32)(16,31)(17,25)
(18,26)(19,28)(20,27)(21,33)(22,34)(23,36)(24,35);;
s2 := ( 1,16)( 2,15)( 3,14)( 4,13)( 5,24)( 6,23)( 7,22)( 8,21)( 9,20)(10,19)
(11,18)(12,17)(25,32)(26,31)(27,30)(28,29)(33,36)(34,35);;
s3 := (37,38);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(38)!( 2, 3)( 6, 7)(10,11)(14,15)(18,19)(22,23)(26,27)(30,31)(34,35);
s1 := Sym(38)!( 3, 4)( 5, 9)( 6,10)( 7,12)( 8,11)(13,29)(14,30)(15,32)(16,31)
(17,25)(18,26)(19,28)(20,27)(21,33)(22,34)(23,36)(24,35);
s2 := Sym(38)!( 1,16)( 2,15)( 3,14)( 4,13)( 5,24)( 6,23)( 7,22)( 8,21)( 9,20)
(10,19)(11,18)(12,17)(25,32)(26,31)(27,30)(28,29)(33,36)(34,35);
s3 := Sym(38)!(37,38);
poly := sub<Sym(38)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2 >; 
 

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