Polytope of Type {2,4,4,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,4,2}*1152
if this polytope has a name.
Group : SmallGroup(1152,134274)
Rank : 5
Schlafli Type : {2,4,4,2}
Number of vertices, edges, etc : 2, 36, 72, 36, 2
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Self-Dual
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 : {2,4,4,2}*576
4-fold quotients : {2,4,4,2}*288
9-fold quotients : {2,4,4,2}*128
18-fold quotients : {2,2,4,2}*64, {2,4,2,2}*64
36-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (10,11)(13,14);;
s2 := ( 3, 9)( 4,10)( 5,11)( 6,12)( 7,13)( 8,14);;
s3 := ( 3, 4)( 6, 7)( 9,12)(10,13)(11,14);;
s4 := (15,16);;
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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(16)!(1,2);
s1 := Sym(16)!(10,11)(13,14);
s2 := Sym(16)!( 3, 9)( 4,10)( 5,11)( 6,12)( 7,13)( 8,14);
s3 := Sym(16)!( 3, 4)( 6, 7)( 9,12)(10,13)(11,14);
s4 := Sym(16)!(15,16);
poly := sub<Sym(16)|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*s1*s0*s1, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2 >;
to this polytope