Polytope of Type {9,2,5}

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

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