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# Polytope of Type {4,2,10,6}

Atlas Canonical Name : {4,2,10,6}*1920c
if this polytope has a name.
Group : SmallGroup(1920,240595)
Rank : 5
Schlafli Type : {4,2,10,6}
Number of vertices, edges, etc : 4, 4, 20, 60, 12
Order of s0s1s2s3s4 : 20
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
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 : {4,2,5,6}*960c, {4,2,10,3}*960b, {2,2,10,6}*960c
4-fold quotients : {4,2,5,3}*480, {2,2,5,6}*480c, {2,2,10,3}*480b
8-fold quotients : {2,2,5,3}*240
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := (6,7)(8,9);;
s3 := ( 5, 6)( 7, 8)(10,11)(12,13);;
s4 := ( 6, 9)( 7, 8)(10,12)(11,13);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s3*s4*s3*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :
s0 := Sym(13)!(2,3);
s1 := Sym(13)!(1,2)(3,4);
s2 := Sym(13)!(6,7)(8,9);
s3 := Sym(13)!( 5, 6)( 7, 8)(10,11)(12,13);
s4 := Sym(13)!( 6, 9)( 7, 8)(10,12)(11,13);
poly := sub<Sym(13)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s3*s4*s3*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s2 >;

to this polytope