Polytope of Type {8,2,10,5}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,2,10,5}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240561)
Rank : 5
Schlafli Type : {8,2,10,5}
Number of vertices, edges, etc : 8, 8, 12, 30, 6
Order of s0s1s2s3s4 : 24
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 : {8,2,5,5}*960, {4,2,10,5}*960b
4-fold quotients : {4,2,5,5}*480, {2,2,10,5}*480b
8-fold quotients : {2,2,5,5}*240
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := ( 9,11)(10,16)(12,20)(13,15)(14,17)(18,19);;
s3 := (11,13)(12,19)(14,20)(15,17);;
s4 := (10,17)(12,20)(13,15)(14,16);;
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,
s2*s3*s4*s2*s3*s4*s2*s3*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(20)!(2,3)(4,5)(6,7);
s1 := Sym(20)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(20)!( 9,11)(10,16)(12,20)(13,15)(14,17)(18,19);
s3 := Sym(20)!(11,13)(12,19)(14,20)(15,17);
s4 := Sym(20)!(10,17)(12,20)(13,15)(14,16);
poly := sub<Sym(20)|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, s2*s3*s4*s2*s3*s4*s2*s3*s4,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
to this polytope