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Polytope of Type {10,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,5}*240
if this polytope has a name.
Group : SmallGroup(240,190)
Rank : 3
Schlafli Type : {10,5}
Number of vertices, edges, etc : 24, 60, 12
Order of s0s1s2 : 6
Order of s0s1s2s1 : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {10,5,2} of size 480
Vertex Figure Of :
   {2,10,5} of size 480
   {4,10,5} of size 960
   {6,10,5} of size 1440
   {8,10,5} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,5}*120, {10,5}*120a, {10,5}*120b
   4-fold quotients : {5,5}*60
Covers (Minimal Covers in Boldface) :
   2-fold covers : {20,5}*480, {10,10}*480
   3-fold covers : {10,15}*720
   4-fold covers : {10,20}*960a, {20,10}*960a, {10,20}*960b, {20,10}*960b, {10,10}*960
   5-fold covers : {10,5}*1200a, {10,5}*1200b
   6-fold covers : {20,15}*1440a, {10,30}*1440, {30,10}*1440
   7-fold covers : {10,35}*1680
   8-fold covers : {20,20}*1920a, {10,40}*1920a, {40,10}*1920a, {10,20}*1920, {20,10}*1920, {20,20}*1920b, {20,20}*1920c, {20,20}*1920d, {10,40}*1920b, {40,10}*1920b
Permutation Representation (GAP) :
s0 := (2,3)(4,5)(6,7)(8,9);;
s1 := (1,2)(3,4)(6,8)(7,9);;
s2 := (2,4)(3,5)(6,8)(7,9);;
poly := Group([s0,s1,s2]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(9)!(2,3)(4,5)(6,7)(8,9);
s1 := Sym(9)!(1,2)(3,4)(6,8)(7,9);
s2 := Sym(9)!(2,4)(3,5)(6,8)(7,9);
poly := sub<Sym(9)|s0,s1,s2>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope