include("/home/bitnami/htdocs/websites/abstract-polytopes/www/subs.php"); ?>
Polytope of Type {2,2,2,8,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,8,4}*512a
if this polytope has a name.
Group : SmallGroup(512,10482002)
Rank : 6
Schlafli Type : {2,2,2,8,4}
Number of vertices, edges, etc : 2, 2, 2, 8, 16, 4
Order of s0s1s2s3s4s5 : 8
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
Degenerate
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 : {2,2,2,4,4}*256, {2,2,2,8,2}*256
4-fold quotients : {2,2,2,2,4}*128, {2,2,2,4,2}*128
8-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := ( 8, 9)(10,12)(11,14)(15,17)(16,18)(19,21);;
s4 := ( 7, 8)( 9,11)(10,13)(12,15)(14,16)(17,19)(18,20)(21,22);;
s5 := ( 8,10)( 9,12)(16,19)(18,21);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s3*s4*s5*s4*s3*s4*s5*s4,
s4*s5*s4*s5*s4*s5*s4*s5, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(22)!(1,2);
s1 := Sym(22)!(3,4);
s2 := Sym(22)!(5,6);
s3 := Sym(22)!( 8, 9)(10,12)(11,14)(15,17)(16,18)(19,21);
s4 := Sym(22)!( 7, 8)( 9,11)(10,13)(12,15)(14,16)(17,19)(18,20)(21,22);
s5 := Sym(22)!( 8,10)( 9,12)(16,19)(18,21);
poly := sub<Sym(22)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s0*s5*s0*s5, s1*s5*s1*s5,
s2*s5*s2*s5, s3*s5*s3*s5, s3*s4*s5*s4*s3*s4*s5*s4,
s4*s5*s4*s5*s4*s5*s4*s5, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope