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Polytope of Type {4,6,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,10}*1920c
if this polytope has a name.
Group : SmallGroup(1920,240592)
Rank : 4
Schlafli Type : {4,6,10}
Number of vertices, edges, etc : 4, 48, 120, 40
Order of s0s1s2s3 : 4
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,6,5}*960a, {4,6,10}*960a, {4,6,10}*960b, {2,6,10}*960b
   4-fold quotients : {4,6,5}*480a, {2,6,5}*480a, {2,6,10}*480a, {2,6,10}*480b
   8-fold quotients : {2,6,5}*240a
   60-fold quotients : {4,2,2}*32
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 2)( 3, 6)( 4,10)( 5,11)( 7, 9)( 8,15)(12,16)(13,14);;
s1 := ( 1,13)( 2, 8)( 3, 7)( 4, 6)( 5,14)( 9,12)(10,16)(11,15)(19,21);;
s2 := ( 1,13)( 2,14)( 3, 7)( 4,12)( 5, 8)( 6, 9)(10,16)(11,15)(17,18)(19,20);;
s3 := ( 1, 3)( 2, 6)( 4, 8)( 5,12)( 7,13)( 9,14)(10,15)(11,16)(18,20)(19,21);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s1*s2*s3*s2*s3*s2*s3*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(21)!( 1, 2)( 3, 6)( 4,10)( 5,11)( 7, 9)( 8,15)(12,16)(13,14);
s1 := Sym(21)!( 1,13)( 2, 8)( 3, 7)( 4, 6)( 5,14)( 9,12)(10,16)(11,15)(19,21);
s2 := Sym(21)!( 1,13)( 2,14)( 3, 7)( 4,12)( 5, 8)( 6, 9)(10,16)(11,15)(17,18)
(19,20);
s3 := Sym(21)!( 1, 3)( 2, 6)( 4, 8)( 5,12)( 7,13)( 9,14)(10,15)(11,16)(18,20)
(19,21);
poly := sub<Sym(21)|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, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s1*s2*s3*s2*s3*s2*s3*s2*s1*s2 >; 
 
References : None.
to this polytope