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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,9,2,2}*576
if this polytope has a name.
Group : SmallGroup(576,8262)
Rank : 6
Schlafli Type : {2,4,9,2,2}
Number of vertices, edges, etc : 2, 4, 18, 9, 2, 2
Order of s0s1s2s3s4s5 : 18
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,4,9,2,2,2} of size 1152
   {2,4,9,2,2,3} of size 1728
Vertex Figure Of :
   {2,2,4,9,2,2} of size 1152
   {3,2,4,9,2,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,4,3,2,2}*192
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,9,2,4}*1152, {2,4,9,2,2}*1152, {2,4,18,2,2}*1152b, {2,4,18,2,2}*1152c
   3-fold covers : {2,4,27,2,2}*1728, {2,4,9,2,6}*1728, {2,4,9,6,2}*1728
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 9)( 5,11)( 6,13)( 7,15)(10,20)(12,22)(16,26)(23,32)(25,34)(27,35)
(29,36)(31,37);;
s2 := ( 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);;
s3 := ( 3, 8)( 4, 6)( 5,16)( 7,12)( 9,13)(10,25)(11,26)(14,21)(15,22)(17,18)
(19,33)(20,34)(23,29)(24,30)(27,31)(28,38)(32,36)(35,37);;
s4 := (39,40);;
s5 := (41,42);;
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s1*s2, 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(42)!(1,2);
s1 := Sym(42)!( 4, 9)( 5,11)( 6,13)( 7,15)(10,20)(12,22)(16,26)(23,32)(25,34)
(27,35)(29,36)(31,37);
s2 := Sym(42)!( 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);
s3 := Sym(42)!( 3, 8)( 4, 6)( 5,16)( 7,12)( 9,13)(10,25)(11,26)(14,21)(15,22)
(17,18)(19,33)(20,34)(23,29)(24,30)(27,31)(28,38)(32,36)(35,37);
s4 := Sym(42)!(39,40);
s5 := Sym(42)!(41,42);
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, 
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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