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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,4,2,4}*576
if this polytope has a name.
Group : SmallGroup(576,4970)
Rank : 5
Schlafli Type : {9,4,2,4}
Number of vertices, edges, etc : 9, 18, 4, 4, 4
Order of s0s1s2s3s4 : 36
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {9,4,2,4,2} of size 1152
   {9,4,2,4,3} of size 1728
Vertex Figure Of :
   {2,9,4,2,4} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {9,4,2,2}*288
   3-fold quotients : {3,4,2,4}*192
   6-fold quotients : {3,4,2,2}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {9,4,2,8}*1152, {9,4,2,4}*1152, {18,4,2,4}*1152b, {18,4,2,4}*1152c
   3-fold covers : {27,4,2,4}*1728, {9,4,2,12}*1728
Permutation Representation (GAP) :
s0 := ( 1, 2)( 3, 6)( 4, 5)( 7,15)( 8,14)( 9,16)(10,12)(11,13)(17,23)(18,24)
(19,21)(20,22)(25,31)(26,32)(27,29)(28,30)(33,36)(34,35);;
s1 := ( 1, 5)( 2, 3)( 4,12)( 6, 8)( 7, 9)(10,21)(11,22)(13,15)(14,17)(16,18)
(19,29)(20,30)(23,25)(24,26)(27,31)(28,35)(32,33)(34,36);;
s2 := ( 1,15)( 2, 7)( 3, 9)( 6,16)(10,20)(12,22)(17,26)(19,28)(21,30)(23,32)
(25,33)(31,36);;
s3 := (38,39);;
s4 := (37,38)(39,40);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s1*s2*s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s1*s0*s2*s1*s2*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(40)!( 1, 2)( 3, 6)( 4, 5)( 7,15)( 8,14)( 9,16)(10,12)(11,13)(17,23)
(18,24)(19,21)(20,22)(25,31)(26,32)(27,29)(28,30)(33,36)(34,35);
s1 := Sym(40)!( 1, 5)( 2, 3)( 4,12)( 6, 8)( 7, 9)(10,21)(11,22)(13,15)(14,17)
(16,18)(19,29)(20,30)(23,25)(24,26)(27,31)(28,35)(32,33)(34,36);
s2 := Sym(40)!( 1,15)( 2, 7)( 3, 9)( 6,16)(10,20)(12,22)(17,26)(19,28)(21,30)
(23,32)(25,33)(31,36);
s3 := Sym(40)!(38,39);
s4 := Sym(40)!(37,38)(39,40);
poly := sub<Sym(40)|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, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4, s2*s1*s0*s2*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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