Polytope of Type {11,2,14}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {11,2,14}*616
if this polytope has a name.
Group : SmallGroup(616,31)
Rank : 4
Schlafli Type : {11,2,14}
Number of vertices, edges, etc : 11, 11, 14, 14
Order of s0s1s2s3 : 154
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{11,2,14,2} of size 1232
Vertex Figure Of :
{2,11,2,14} of size 1232
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {11,2,7}*308
7-fold quotients : {11,2,2}*88
Covers (Minimal Covers in Boldface) :
2-fold covers : {11,2,28}*1232, {22,2,14}*1232
3-fold covers : {11,2,42}*1848, {33,2,14}*1848
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10);;
s2 := (14,15)(16,17)(18,19)(20,21)(22,23)(24,25);;
s3 := (12,16)(13,14)(15,20)(17,18)(19,24)(21,22)(23,25);;
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,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(25)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11);
s1 := Sym(25)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10);
s2 := Sym(25)!(14,15)(16,17)(18,19)(20,21)(22,23)(24,25);
s3 := Sym(25)!(12,16)(13,14)(15,20)(17,18)(19,24)(21,22)(23,25);
poly := sub<Sym(25)|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, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope