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

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

to this polytope