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Polytope of Type {4,12,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,10}*1920g
if this polytope has a name.
Group : SmallGroup(1920,240508)
Rank : 4
Schlafli Type : {4,12,10}
Number of vertices, edges, etc : 4, 48, 120, 20
Order of s0s1s2s3 : 20
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Universal
   Non-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 : {4,6,10}*960d, {2,12,10}*960d
   4-fold quotients : {4,6,5}*480b, {2,6,10}*480e
   8-fold quotients : {2,3,10}*240a, {2,6,5}*240b
   16-fold quotients : {2,3,5}*120
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,6)(2,8)(3,7)(4,5);;
s1 := ( 1, 8)( 2, 5)( 3, 4)( 6, 7)(10,11)(12,13);;
s2 := ( 1, 6)( 2, 7)( 3, 8)( 4, 5)( 9,12)(10,11);;
s3 := ( 1, 5)( 2, 8)( 3, 7)( 4, 6)(10,12)(11,13);;
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, s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
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(13)!(1,6)(2,8)(3,7)(4,5);
s1 := Sym(13)!( 1, 8)( 2, 5)( 3, 4)( 6, 7)(10,11)(12,13);
s2 := Sym(13)!( 1, 6)( 2, 7)( 3, 8)( 4, 5)( 9,12)(10,11);
s3 := Sym(13)!( 1, 5)( 2, 8)( 3, 7)( 4, 6)(10,12)(11,13);
poly := sub<Sym(13)|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, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 
References : None.
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