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Polytope of Type {10,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,6}*480c
if this polytope has a name.
Group : SmallGroup(480,1187)
Rank : 3
Schlafli Type : {10,6}
Number of vertices, edges, etc : 40, 120, 24
Order of s0s1s2 : 10
Order of s0s1s2s1 : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {10,6,2} of size 960
   {10,6,4} of size 1920
Vertex Figure Of :
   {2,10,6} of size 960
   {4,10,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,6}*240b, {10,3}*240, {10,6}*240c, {10,6}*240d, {10,6}*240e, {10,6}*240f
   4-fold quotients : {5,3}*120, {5,6}*120b, {5,6}*120c, {10,3}*120a, {10,3}*120b
   8-fold quotients : {5,3}*60
   60-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {10,12}*960c, {20,6}*960c, {10,12}*960d, {20,6}*960d, {10,6}*960b
   3-fold covers : {10,6}*1440f, {30,6}*1440e, {30,6}*1440f
   4-fold covers : {20,12}*1920g, {10,24}*1920d, {40,6}*1920f, {10,12}*1920c, {20,6}*1920d, {20,12}*1920k, {20,12}*1920l, {20,12}*1920m, {10,24}*1920f, {40,6}*1920h
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 6)( 8, 9)(10,11);;
s1 := ( 3, 5)( 4, 6)( 7, 8)( 9,10);;
s2 := ( 1, 2)( 8,11)( 9,10);;
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, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(11)!( 3, 4)( 5, 6)( 8, 9)(10,11);
s1 := Sym(11)!( 3, 5)( 4, 6)( 7, 8)( 9,10);
s2 := Sym(11)!( 1, 2)( 8,11)( 9,10);
poly := sub<Sym(11)|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, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
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