Polytope of Type {9,2,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,2,10}*360
if this polytope has a name.
Group : SmallGroup(360,45)
Rank : 4
Schlafli Type : {9,2,10}
Number of vertices, edges, etc : 9, 9, 10, 10
Order of s₀s₁s₂s₃ : 90
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {9,2,10,2} of size 720
   {9,2,10,4} of size 1440
   {9,2,10,5} of size 1800
Vertex Figure Of :
   {2,9,2,10} of size 720
   {4,9,2,10} of size 1440
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {9,2,5}*180
   3-fold quotients : {3,2,10}*120
   5-fold quotients : {9,2,2}*72
   6-fold quotients : {3,2,5}*60
   15-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {9,2,20}*720, {18,2,10}*720
   3-fold covers : {27,2,10}*1080, {9,6,10}*1080, {9,2,30}*1080
   4-fold covers : {9,2,40}*1440, {36,2,10}*1440, {18,2,20}*1440, {18,4,10}*1440, {9,4,10}*1440
   5-fold covers : {9,2,50}*1800, {45,2,10}*1800
Permutation Representation (GAP) :

s0 := (2,3)(4,5)(6,7)(8,9);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (12,13)(14,15)(16,17)(18,19);;
s3 := (10,14)(11,12)(13,18)(15,16)(17,19);;
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*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*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(19)!(2,3)(4,5)(6,7)(8,9);
s1 := Sym(19)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(19)!(12,13)(14,15)(16,17)(18,19);
s3 := Sym(19)!(10,14)(11,12)(13,18)(15,16)(17,19);
poly := sub<Sym(19)|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*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*s2*s3 >;

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