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

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

s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 8, 9)(10,11);;
s2 := ( 3, 4)( 5, 6)( 7, 8)( 9,10);;
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*s1*s0*s1, 
s0*s2*s0*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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(15)!(1,2);
s1 := Sym(15)!( 4, 5)( 6, 7)( 8, 9)(10,11);
s2 := Sym(15)!( 3, 4)( 5, 6)( 7, 8)( 9,10);
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*s1*s0*s1, s0*s2*s0*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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope