Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,20,5}

Atlas Canonical Name {2,20,5}*960

Overview

Group
SmallGroup(960,10889)
Rank
4
Schläfli Type
{2,20,5}
Vertices, edges, …
2, 48, 120, 12
Order of s0s1s2s3
12
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

Covers minimal covers in bold

2-fold

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := ( 4,12)( 5,14)( 6,19)( 7,21)( 9,40)(13,30)(15,46)(16,45)(17,36)(22,25)(23,38)(24,39)(26,28)(31,35)(32,33)(34,37)(41,49)(42,48)(43,47)(44,50);;
s2 := ( 3, 6)( 4,15)( 5,10)( 7,18)( 8,19)( 9,45)(11,32)(12,37)(13,29)(14,24)(16,26)(17,27)(20,21)(22,48)(23,30)(25,35)(28,31)(33,42)(34,41)(36,44)(38,40)(39,49)(43,46)(47,50);;
s3 := ( 3,10)( 4, 6)( 5,35)( 7,26)( 8,27)( 9,23)(11,18)(12,19)(13,34)(14,31)(15,33)(16,36)(17,45)(20,29)(21,28)(22,48)(24,41)(25,42)(30,37)(32,46)(38,40)(39,49)(43,44)(47,50);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2, 
s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(50)!(1,2);
s1 := Sym(50)!( 4,12)( 5,14)( 6,19)( 7,21)( 9,40)(13,30)(15,46)(16,45)(17,36)(22,25)(23,38)(24,39)(26,28)(31,35)(32,33)(34,37)(41,49)(42,48)(43,47)(44,50);
s2 := Sym(50)!( 3, 6)( 4,15)( 5,10)( 7,18)( 8,19)( 9,45)(11,32)(12,37)(13,29)(14,24)(16,26)(17,27)(20,21)(22,48)(23,30)(25,35)(28,31)(33,42)(34,41)(36,44)(38,40)(39,49)(43,46)(47,50);
s3 := Sym(50)!( 3,10)( 4, 6)( 5,35)( 7,26)( 8,27)( 9,23)(11,18)(12,19)(13,34)(14,31)(15,33)(16,36)(17,45)(20,29)(21,28)(22,48)(24,41)(25,42)(30,37)(32,46)(38,40)(39,49)(43,44)(47,50);
poly := sub<Sym(50)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2, 
s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2 >;