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

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

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