Part of the Atlas of Small Regular Polytopes

Polytope of Type {20,6,2}

Atlas Canonical Name {20,6,2}*720

Overview

Group
SmallGroup(720,810)
Rank
4
Schläfli Type
{20,6,2}
Vertices, edges, …
30, 90, 9, 2
Order of s0s1s2s3
20
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

5-fold

Covers minimal covers in bold

2-fold

Representations

Permutation Representation (GAP) 
s0 := ( 2, 5)( 3, 4)( 6,16)( 7,20)( 8,19)( 9,18)(10,17)(11,31)(12,35)(13,34)(14,33)(15,32)(22,25)(23,24)(26,36)(27,40)(28,39)(29,38)(30,37)(42,45)(43,44);;
s1 := ( 1, 2)( 3, 5)( 6,12)( 7,11)( 8,15)( 9,14)(10,13)(16,17)(18,20)(21,27)(22,26)(23,30)(24,29)(25,28)(31,32)(33,35)(36,42)(37,41)(38,45)(39,44)(40,43);;
s2 := ( 1,21)( 2,22)( 3,23)( 4,24)( 5,25)( 6,16)( 7,17)( 8,18)( 9,19)(10,20)(11,26)(12,27)(13,28)(14,29)(15,30)(31,36)(32,37)(33,38)(34,39)(35,40);;
s3 := (46,47);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(47)!( 2, 5)( 3, 4)( 6,16)( 7,20)( 8,19)( 9,18)(10,17)(11,31)(12,35)(13,34)(14,33)(15,32)(22,25)(23,24)(26,36)(27,40)(28,39)(29,38)(30,37)(42,45)(43,44);
s1 := Sym(47)!( 1, 2)( 3, 5)( 6,12)( 7,11)( 8,15)( 9,14)(10,13)(16,17)(18,20)(21,27)(22,26)(23,30)(24,29)(25,28)(31,32)(33,35)(36,42)(37,41)(38,45)(39,44)(40,43);
s2 := Sym(47)!( 1,21)( 2,22)( 3,23)( 4,24)( 5,25)( 6,16)( 7,17)( 8,18)( 9,19)(10,20)(11,26)(12,27)(13,28)(14,29)(15,30)(31,36)(32,37)(33,38)(34,39)(35,40);
s3 := Sym(47)!(46,47);
poly := sub<Sym(47)|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, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2 >;