Polytope of Type {5,2,9}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,9}*180
if this polytope has a name.
Group : SmallGroup(180,7)
Rank : 4
Schlafli Type : {5,2,9}
Number of vertices, edges, etc : 5, 5, 9, 9
Order of s₀s₁s₂s₃ : 45
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,2,9,2} of size 360
   {5,2,9,4} of size 720
   {5,2,9,6} of size 1080
   {5,2,9,4} of size 1440
Vertex Figure Of :
   {2,5,2,9} of size 360
   {3,5,2,9} of size 1080
   {5,5,2,9} of size 1080
   {10,5,2,9} of size 1800
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {5,2,3}*60
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,2,18}*360, {10,2,9}*360
   3-fold covers : {5,2,27}*540, {15,2,9}*540
   4-fold covers : {5,2,36}*720, {20,2,9}*720, {10,2,18}*720
   5-fold covers : {25,2,9}*900, {5,2,45}*900
   6-fold covers : {5,2,54}*1080, {10,2,27}*1080, {10,6,9}*1080, {15,2,18}*1080, {30,2,9}*1080
   7-fold covers : {5,2,63}*1260, {35,2,9}*1260
   8-fold covers : {5,2,72}*1440, {40,2,9}*1440, {10,2,36}*1440, {20,2,18}*1440, {10,4,18}*1440, {10,4,9}*1440
   9-fold covers : {5,2,81}*1620, {45,2,9}*1620, {15,6,9}*1620, {15,2,27}*1620
   10-fold covers : {25,2,18}*1800, {50,2,9}*1800, {5,10,18}*1800, {5,2,90}*1800, {10,2,45}*1800
   11-fold covers : {5,2,99}*1980, {55,2,9}*1980
Permutation Representation (GAP) :

s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := ( 7, 8)( 9,10)(11,12)(13,14);;
s3 := ( 6, 7)( 8, 9)(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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(14)!(2,3)(4,5);
s1 := Sym(14)!(1,2)(3,4);
s2 := Sym(14)!( 7, 8)( 9,10)(11,12)(13,14);
s3 := Sym(14)!( 6, 7)( 8, 9)(10,11)(12,13);
poly := sub<Sym(14)|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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope