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Polytope of Type {4,2,9}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,9}*144
if this polytope has a name.
Group : SmallGroup(144,41)
Rank : 4
Schlafli Type : {4,2,9}
Number of vertices, edges, etc : 4, 4, 9, 9
Order of s0s1s2s3 : 36
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,2,9,2} of size 288
   {4,2,9,4} of size 576
   {4,2,9,6} of size 864
   {4,2,9,4} of size 1152
Vertex Figure Of :
   {2,4,2,9} of size 288
   {3,4,2,9} of size 432
   {4,4,2,9} of size 576
   {6,4,2,9} of size 864
   {3,4,2,9} of size 864
   {6,4,2,9} of size 864
   {6,4,2,9} of size 864
   {8,4,2,9} of size 1152
   {8,4,2,9} of size 1152
   {4,4,2,9} of size 1152
   {9,4,2,9} of size 1296
   {4,4,2,9} of size 1296
   {6,4,2,9} of size 1296
   {10,4,2,9} of size 1440
   {12,4,2,9} of size 1728
   {12,4,2,9} of size 1728
   {12,4,2,9} of size 1728
   {6,4,2,9} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,9}*72
   3-fold quotients : {4,2,3}*48
   6-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,2,9}*288, {4,2,18}*288
   3-fold covers : {4,2,27}*432, {12,2,9}*432, {4,6,9}*432
   4-fold covers : {16,2,9}*576, {4,2,36}*576, {4,4,18}*576, {8,2,18}*576, {4,4,9}*576b
   5-fold covers : {20,2,9}*720, {4,2,45}*720
   6-fold covers : {8,2,27}*864, {4,2,54}*864, {24,2,9}*864, {8,6,9}*864, {12,2,18}*864, {4,6,18}*864a, {4,6,18}*864b
   7-fold covers : {28,2,9}*1008, {4,2,63}*1008
   8-fold covers : {32,2,9}*1152, {4,4,36}*1152, {4,8,18}*1152a, {8,4,18}*1152a, {4,8,18}*1152b, {8,4,18}*1152b, {4,4,18}*1152a, {8,2,36}*1152, {4,2,72}*1152, {16,2,18}*1152, {4,8,9}*1152, {8,4,9}*1152, {4,4,18}*1152d
   9-fold covers : {4,2,81}*1296, {36,2,9}*1296, {12,6,9}*1296a, {12,2,27}*1296, {4,18,9}*1296, {4,6,9}*1296a, {4,6,27}*1296, {12,6,9}*1296b, {4,6,9}*1296e
   10-fold covers : {40,2,9}*1440, {8,2,45}*1440, {20,2,18}*1440, {4,10,18}*1440, {4,2,90}*1440
   11-fold covers : {44,2,9}*1584, {4,2,99}*1584
   12-fold covers : {16,2,27}*1728, {4,2,108}*1728, {4,4,54}*1728, {8,2,54}*1728, {48,2,9}*1728, {16,6,9}*1728, {4,4,27}*1728b, {12,2,36}*1728, {4,6,36}*1728a, {4,12,18}*1728a, {12,4,18}*1728, {24,2,18}*1728, {8,6,18}*1728a, {4,6,36}*1728b, {8,6,18}*1728b, {4,12,18}*1728b, {4,6,9}*1728a, {12,4,9}*1728, {4,12,9}*1728
   13-fold covers : {52,2,9}*1872, {4,2,117}*1872
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 6, 7)( 8, 9)(10,11)(12,13);;
s3 := ( 5, 6)( 7, 8)( 9,10)(11,12);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, 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(13)!(2,3);
s1 := Sym(13)!(1,2)(3,4);
s2 := Sym(13)!( 6, 7)( 8, 9)(10,11)(12,13);
s3 := Sym(13)!( 5, 6)( 7, 8)( 9,10)(11,12);
poly := sub<Sym(13)|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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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