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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,18,2}*288
if this polytope has a name.
Group : SmallGroup(288,839)
Rank : 5
Schlafli Type : {2,2,18,2}
Number of vertices, edges, etc : 2, 2, 18, 18, 2
Order of s0s1s2s3s4 : 18
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,18,2,2} of size 576
   {2,2,18,2,3} of size 864
   {2,2,18,2,4} of size 1152
   {2,2,18,2,5} of size 1440
   {2,2,18,2,6} of size 1728
Vertex Figure Of :
   {2,2,2,18,2} of size 576
   {3,2,2,18,2} of size 864
   {4,2,2,18,2} of size 1152
   {5,2,2,18,2} of size 1440
   {6,2,2,18,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,9,2}*144
   3-fold quotients : {2,2,6,2}*96
   6-fold quotients : {2,2,3,2}*48
   9-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,2,36,2}*576, {2,2,18,4}*576a, {2,4,18,2}*576a, {4,2,18,2}*576
   3-fold covers : {2,2,54,2}*864, {2,2,18,6}*864a, {2,2,18,6}*864b, {2,6,18,2}*864a, {2,6,18,2}*864b, {6,2,18,2}*864
   4-fold covers : {4,4,18,2}*1152, {2,2,36,4}*1152a, {2,4,36,2}*1152a, {4,2,18,4}*1152a, {2,4,18,4}*1152a, {4,2,36,2}*1152, {2,2,18,8}*1152, {2,8,18,2}*1152, {8,2,18,2}*1152, {2,2,72,2}*1152, {2,2,18,4}*1152, {2,4,18,2}*1152
   5-fold covers : {2,2,18,10}*1440, {2,10,18,2}*1440, {10,2,18,2}*1440, {2,2,90,2}*1440
   6-fold covers : {2,2,108,2}*1728, {2,2,54,4}*1728a, {2,4,54,2}*1728a, {4,2,54,2}*1728, {2,2,18,12}*1728a, {2,12,18,2}*1728a, {12,2,18,2}*1728, {2,2,36,6}*1728a, {2,2,36,6}*1728b, {2,6,36,2}*1728a, {2,6,36,2}*1728b, {6,2,36,2}*1728, {2,4,18,6}*1728a, {2,4,18,6}*1728b, {2,6,18,4}*1728a, {2,6,18,4}*1728b, {4,2,18,6}*1728a, {4,2,18,6}*1728b, {4,6,18,2}*1728a, {6,2,18,4}*1728a, {6,4,18,2}*1728, {2,2,18,12}*1728b, {2,12,18,2}*1728b, {4,6,18,2}*1728b
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22);;
s3 := ( 5, 9)( 6, 7)( 8,13)(10,11)(12,17)(14,15)(16,21)(18,19)(20,22);;
s4 := (23,24);;
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*s1*s0*s1, 
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, s3*s4*s3*s4, 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(24)!(1,2);
s1 := Sym(24)!(3,4);
s2 := Sym(24)!( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22);
s3 := Sym(24)!( 5, 9)( 6, 7)( 8,13)(10,11)(12,17)(14,15)(16,21)(18,19)(20,22);
s4 := Sym(24)!(23,24);
poly := sub<Sym(24)|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*s1*s0*s1, 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, 
s3*s4*s3*s4, 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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