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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}*1440f
if this polytope has a name.
Group : SmallGroup(1440,5853)
Rank : 3
Schlafli Type : {10,6}
Number of vertices, edges, etc : 120, 360, 72
Order of s0s1s2 : 30
Order of s0s1s2s1 : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,3}*720b, {10,6}*720b, {10,6}*720c
   3-fold quotients : {10,6}*480c
   4-fold quotients : {10,3}*360
   6-fold quotients : {5,6}*240b, {10,3}*240, {10,6}*240c, {10,6}*240d, {10,6}*240e, {10,6}*240f
   12-fold quotients : {5,3}*120, {5,6}*120b, {5,6}*120c, {10,3}*120a, {10,3}*120b
   24-fold quotients : {5,3}*60
   60-fold quotients : {2,6}*24
   120-fold quotients : {2,3}*12
   180-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 6)( 4, 5)( 7,10)( 8, 9)(11,14)(12,15)(13,16);;
s1 := ( 1, 3)( 2, 4)( 5, 8)( 6, 7)(12,16)(13,15);;
s2 := ( 1, 2)( 3, 9)( 4,10)( 5, 7)( 6, 8)(11,12)(13,16)(14,15);;
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, 
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(16)!( 3, 6)( 4, 5)( 7,10)( 8, 9)(11,14)(12,15)(13,16);
s1 := Sym(16)!( 1, 3)( 2, 4)( 5, 8)( 6, 7)(12,16)(13,15);
s2 := Sym(16)!( 1, 2)( 3, 9)( 4,10)( 5, 7)( 6, 8)(11,12)(13,16)(14,15);
poly := sub<Sym(16)|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, 
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
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