Polytope of Type {9,2,4}

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

s0 := (2,3)(4,5)(6,7)(8,9);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (11,12);;
s3 := (10,11)(12,13);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3, 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(13)!(2,3)(4,5)(6,7)(8,9);
s1 := Sym(13)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(13)!(11,12);
s3 := Sym(13)!(10,11)(12,13);
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, s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope