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Polytope of Type {9,2,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,2,2,3}*216
if this polytope has a name.
Group : SmallGroup(216,101)
Rank : 5
Schlafli Type : {9,2,2,3}
Number of vertices, edges, etc : 9, 9, 2, 3, 3
Order of s0s1s2s3s4 : 18
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {9,2,2,3,2} of size 432
   {9,2,2,3,3} of size 864
   {9,2,2,3,4} of size 864
   {9,2,2,3,6} of size 1296
   {9,2,2,3,4} of size 1728
   {9,2,2,3,6} of size 1728
Vertex Figure Of :
   {2,9,2,2,3} of size 432
   {4,9,2,2,3} of size 864
   {6,9,2,2,3} of size 1296
   {4,9,2,2,3} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {3,2,2,3}*72
Covers (Minimal Covers in Boldface) :
   2-fold covers : {9,2,2,6}*432, {18,2,2,3}*432
   3-fold covers : {9,2,2,9}*648, {27,2,2,3}*648, {9,2,6,3}*648, {9,6,2,3}*648
   4-fold covers : {36,2,2,3}*864, {9,2,2,12}*864, {9,2,4,6}*864a, {18,4,2,3}*864a, {9,2,4,3}*864, {9,4,2,3}*864, {18,2,2,6}*864
   5-fold covers : {45,2,2,3}*1080, {9,2,2,15}*1080
   6-fold covers : {9,2,2,18}*1296, {18,2,2,9}*1296, {27,2,2,6}*1296, {54,2,2,3}*1296, {9,2,6,6}*1296a, {9,2,6,6}*1296b, {9,6,2,6}*1296, {18,2,6,3}*1296, {18,6,2,3}*1296a, {18,6,2,3}*1296b
   7-fold covers : {63,2,2,3}*1512, {9,2,2,21}*1512
   8-fold covers : {9,2,4,12}*1728a, {36,4,2,3}*1728a, {72,2,2,3}*1728, {9,2,2,24}*1728, {9,2,8,6}*1728, {18,8,2,3}*1728, {9,2,8,3}*1728, {9,8,2,3}*1728, {18,2,2,12}*1728, {36,2,2,6}*1728, {18,2,4,6}*1728a, {18,4,2,6}*1728a, {9,2,4,6}*1728, {18,2,4,3}*1728, {9,4,2,6}*1728, {18,4,2,3}*1728
   9-fold covers : {9,2,2,27}*1944, {27,2,2,9}*1944, {81,2,2,3}*1944, {9,2,6,9}*1944, {9,6,2,9}*1944, {9,18,2,3}*1944, {9,6,2,3}*1944a, {9,2,6,3}*1944, {27,2,6,3}*1944, {27,6,2,3}*1944, {9,6,6,3}*1944
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 := (13,14);;
s4 := (12,13);;
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*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(14)!(2,3)(4,5)(6,7)(8,9);
s1 := Sym(14)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(14)!(10,11);
s3 := Sym(14)!(13,14);
s4 := Sym(14)!(12,13);
poly := sub<Sym(14)|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*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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