Polytope of Type {2,9,4,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,9,4,2,3}*864
if this polytope has a name.
Group : SmallGroup(864,3999)
Rank : 6
Schlafli Type : {2,9,4,2,3}
Number of vertices, edges, etc : 2, 9, 18, 4, 3, 3
Order of s0s1s2s3s4s5 : 18
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,9,4,2,3,2} of size 1728
Vertex Figure Of :
   {2,2,9,4,2,3} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,3,4,2,3}*288
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,9,4,2,3}*1728, {2,9,4,2,6}*1728, {2,18,4,2,3}*1728b, {2,18,4,2,3}*1728c
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3, 4)( 5, 8)( 6, 7)( 9,17)(10,16)(11,18)(12,14)(13,15)(19,25)(20,26)
(21,23)(22,24)(27,33)(28,34)(29,31)(30,32)(35,38)(36,37);;
s2 := ( 3, 7)( 4, 5)( 6,14)( 8,10)( 9,11)(12,23)(13,24)(15,17)(16,19)(18,20)
(21,31)(22,32)(25,27)(26,28)(29,33)(30,37)(34,35)(36,38);;
s3 := ( 3,17)( 4, 9)( 5,11)( 8,18)(12,22)(14,24)(19,28)(21,30)(23,32)(25,34)
(27,35)(33,38);;
s4 := (40,41);;
s5 := (39,40);;
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, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5*s4*s5, s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s2*s1*s3*s2*s3*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(41)!(1,2);
s1 := Sym(41)!( 3, 4)( 5, 8)( 6, 7)( 9,17)(10,16)(11,18)(12,14)(13,15)(19,25)
(20,26)(21,23)(22,24)(27,33)(28,34)(29,31)(30,32)(35,38)(36,37);
s2 := Sym(41)!( 3, 7)( 4, 5)( 6,14)( 8,10)( 9,11)(12,23)(13,24)(15,17)(16,19)
(18,20)(21,31)(22,32)(25,27)(26,28)(29,33)(30,37)(34,35)(36,38);
s3 := Sym(41)!( 3,17)( 4, 9)( 5,11)( 8,18)(12,22)(14,24)(19,28)(21,30)(23,32)
(25,34)(27,35)(33,38);
s4 := Sym(41)!(40,41);
s5 := Sym(41)!(39,40);
poly := sub<Sym(41)|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, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5*s4*s5, s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s2*s1*s3*s2*s3*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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