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Polytope of Type {8,10,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,10,10}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240561)
Rank : 4
Schlafli Type : {8,10,10}
Number of vertices, edges, etc : 8, 48, 60, 12
Order of s0s1s2s3 : 24
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 : {8,10,5}*960, {4,10,10}*960b
4-fold quotients : {4,10,5}*480, {2,10,10}*480c
8-fold quotients : {2,5,10}*240a, {2,10,5}*240a
16-fold quotients : {2,5,5}*120
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,11)( 2, 9)( 3,15)( 4,13)( 5, 7)( 6,16)( 8,14)(10,12);;
s1 := ( 1, 3)( 2, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(18,21)(19,20);;
s2 := ( 1, 2)( 3, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(17,20)(19,21);;
s3 := (18,19)(20,21);;
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*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s3*s2*s1*s3*s2*s3*s2,
s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(21)!( 1,11)( 2, 9)( 3,15)( 4,13)( 5, 7)( 6,16)( 8,14)(10,12);
s1 := Sym(21)!( 1, 3)( 2, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(18,21)
(19,20);
s2 := Sym(21)!( 1, 2)( 3, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(17,20)
(19,21);
s3 := Sym(21)!(18,19)(20,21);
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*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s3*s2*s1*s3*s2*s3*s2,
s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope