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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,9}*144
if this polytope has a name.
Group : SmallGroup(144,112)
Rank : 5
Schlafli Type : {2,2,2,9}
Number of vertices, edges, etc : 2, 2, 2, 9, 9
Order of s0s1s2s3s4 : 18
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,2,9,2} of size 288
   {2,2,2,9,4} of size 576
   {2,2,2,9,6} of size 864
   {2,2,2,9,4} of size 1152
Vertex Figure Of :
   {2,2,2,2,9} of size 288
   {3,2,2,2,9} of size 432
   {4,2,2,2,9} of size 576
   {5,2,2,2,9} of size 720
   {6,2,2,2,9} of size 864
   {7,2,2,2,9} of size 1008
   {8,2,2,2,9} of size 1152
   {9,2,2,2,9} of size 1296
   {10,2,2,2,9} of size 1440
   {11,2,2,2,9} of size 1584
   {12,2,2,2,9} of size 1728
   {13,2,2,2,9} of size 1872
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,2,9}*288, {4,2,2,9}*288, {2,2,2,18}*288
   3-fold covers : {2,2,2,27}*432, {2,2,6,9}*432, {2,6,2,9}*432, {6,2,2,9}*432
   4-fold covers : {4,4,2,9}*576, {2,8,2,9}*576, {8,2,2,9}*576, {2,2,2,36}*576, {2,2,4,18}*576a, {2,4,2,18}*576, {4,2,2,18}*576, {2,2,4,9}*576
   5-fold covers : {2,10,2,9}*720, {10,2,2,9}*720, {2,2,2,45}*720
   6-fold covers : {2,4,2,27}*864, {4,2,2,27}*864, {2,2,2,54}*864, {2,12,2,9}*864, {12,2,2,9}*864, {4,2,6,9}*864, {4,6,2,9}*864a, {6,4,2,9}*864a, {2,4,6,9}*864, {2,2,6,18}*864a, {2,2,6,18}*864b, {2,6,2,18}*864, {6,2,2,18}*864
   7-fold covers : {2,14,2,9}*1008, {14,2,2,9}*1008, {2,2,2,63}*1008
   8-fold covers : {4,8,2,9}*1152a, {8,4,2,9}*1152a, {4,8,2,9}*1152b, {8,4,2,9}*1152b, {4,4,2,9}*1152, {2,16,2,9}*1152, {16,2,2,9}*1152, {2,4,4,18}*1152, {4,4,2,18}*1152, {2,2,4,36}*1152a, {4,2,4,18}*1152a, {2,4,2,36}*1152, {4,2,2,36}*1152, {2,2,8,18}*1152, {2,8,2,18}*1152, {8,2,2,18}*1152, {2,2,2,72}*1152, {2,4,4,9}*1152b, {4,2,4,9}*1152, {2,2,8,9}*1152, {2,2,4,18}*1152
   9-fold covers : {2,2,2,81}*1296, {2,2,18,9}*1296, {2,18,2,9}*1296, {18,2,2,9}*1296, {2,2,6,9}*1296a, {2,6,6,9}*1296a, {2,2,6,27}*1296, {2,6,2,27}*1296, {6,2,2,27}*1296, {2,6,6,9}*1296b, {6,2,6,9}*1296, {6,6,2,9}*1296a, {6,6,2,9}*1296b, {6,6,2,9}*1296c
   10-fold covers : {2,20,2,9}*1440, {20,2,2,9}*1440, {4,10,2,9}*1440, {10,4,2,9}*1440, {2,4,2,45}*1440, {4,2,2,45}*1440, {2,2,10,18}*1440, {2,10,2,18}*1440, {10,2,2,18}*1440, {2,2,2,90}*1440
   11-fold covers : {2,22,2,9}*1584, {22,2,2,9}*1584, {2,2,2,99}*1584
   12-fold covers : {4,4,2,27}*1728, {2,8,2,27}*1728, {8,2,2,27}*1728, {2,2,2,108}*1728, {2,2,4,54}*1728a, {2,4,2,54}*1728, {4,2,2,54}*1728, {4,12,2,9}*1728a, {12,4,2,9}*1728a, {2,24,2,9}*1728, {24,2,2,9}*1728, {6,8,2,9}*1728, {8,2,6,9}*1728, {8,6,2,9}*1728, {2,8,6,9}*1728, {4,4,6,9}*1728, {2,2,4,27}*1728, {2,2,12,18}*1728a, {2,12,2,18}*1728, {12,2,2,18}*1728, {2,2,6,36}*1728a, {2,2,6,36}*1728b, {2,6,2,36}*1728, {6,2,2,36}*1728, {2,4,6,18}*1728a, {2,6,4,18}*1728, {4,2,6,18}*1728a, {4,2,6,18}*1728b, {4,6,2,18}*1728a, {6,2,4,18}*1728a, {6,4,2,18}*1728a, {2,2,12,18}*1728b, {2,4,6,18}*1728b, {2,2,6,9}*1728, {4,6,2,9}*1728, {6,4,2,9}*1728, {6,6,2,9}*1728, {2,2,12,9}*1728, {2,6,4,9}*1728, {6,2,4,9}*1728
   13-fold covers : {2,26,2,9}*1872, {26,2,2,9}*1872, {2,2,2,117}*1872
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := ( 8, 9)(10,11)(12,13)(14,15);;
s4 := ( 7, 8)( 9,10)(11,12)(13,14);;
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, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(15)!(1,2);
s1 := Sym(15)!(3,4);
s2 := Sym(15)!(5,6);
s3 := Sym(15)!( 8, 9)(10,11)(12,13)(14,15);
s4 := Sym(15)!( 7, 8)( 9,10)(11,12)(13,14);
poly := sub<Sym(15)|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, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

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