Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,2,2,2,2,5,2,2}

Atlas Canonical Name {3,2,2,2,2,5,2,2}*1920

Overview

Group
SmallGroup(1920,236344)
Rank
9
Schläfli Type
{3,2,2,2,2,5,2,2}
Vertices, edges, …
3, 3, 2, 2, 2, 5, 5, 2, 2
Order of s0s1s2s3s4s5s6s7s8
30
Order of s0s1s2s3s4s5s6s7s8s7s6s5s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

No regular quotients.

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (2,3);;
s1 := (1,2);;
s2 := (4,5);;
s3 := (6,7);;
s4 := (8,9);;
s5 := (11,12)(13,14);;
s6 := (10,11)(12,13);;
s7 := (15,16);;
s8 := (17,18);;
poly := Group([s0,s1,s2,s3,s4,s5,s6,s7,s8]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4","s5","s6","s7","s8");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  s6 := F.7;;  s7 := F.8;;  s8 := F.9;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s6*s6, s7*s7, s8*s8, 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, 
s3*s4*s3*s4, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5, 
s0*s6*s0*s6, s1*s6*s1*s6, s2*s6*s2*s6, 
s3*s6*s3*s6, s4*s6*s4*s6, s0*s7*s0*s7, 
s1*s7*s1*s7, s2*s7*s2*s7, s3*s7*s3*s7, 
s4*s7*s4*s7, s5*s7*s5*s7, s6*s7*s6*s7, 
s0*s8*s0*s8, s1*s8*s1*s8, s2*s8*s2*s8, 
s3*s8*s3*s8, s4*s8*s4*s8, s5*s8*s5*s8, 
s6*s8*s6*s8, s7*s8*s7*s8, s0*s1*s0*s1*s0*s1, 
s5*s6*s5*s6*s5*s6*s5*s6*s5*s6 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(18)!(2,3);
s1 := Sym(18)!(1,2);
s2 := Sym(18)!(4,5);
s3 := Sym(18)!(6,7);
s4 := Sym(18)!(8,9);
s5 := Sym(18)!(11,12)(13,14);
s6 := Sym(18)!(10,11)(12,13);
s7 := Sym(18)!(15,16);
s8 := Sym(18)!(17,18);
poly := sub<Sym(18)|s0,s1,s2,s3,s4,s5,s6,s7,s8>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4,s5,s6,s7,s8> := Group< s0,s1,s2,s3,s4,s5,s6,s7,s8 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s6*s6, s7*s7, s8*s8, 
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, s3*s4*s3*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5, s0*s6*s0*s6, 
s1*s6*s1*s6, s2*s6*s2*s6, s3*s6*s3*s6, 
s4*s6*s4*s6, s0*s7*s0*s7, s1*s7*s1*s7, 
s2*s7*s2*s7, s3*s7*s3*s7, s4*s7*s4*s7, 
s5*s7*s5*s7, s6*s7*s6*s7, s0*s8*s0*s8, 
s1*s8*s1*s8, s2*s8*s2*s8, s3*s8*s3*s8, 
s4*s8*s4*s8, s5*s8*s5*s8, s6*s8*s6*s8, 
s7*s8*s7*s8, s0*s1*s0*s1*s0*s1, s5*s6*s5*s6*s5*s6*s5*s6*s5*s6 >;