Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,5,12}

Atlas Canonical Name {2,5,12}*960

Overview

Group
SmallGroup(960,10889)
Rank
4
Schläfli Type
{2,5,12}
Vertices, edges, …
2, 20, 120, 48
Order of s0s1s2s3
20
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 := ( 4, 5)( 6,19)( 7,21)( 9,30)(10,37)(11,31)(12,17)(13,28)(14,41)(15,27)(16,29)(22,40)(23,35)(24,46)(25,33)(26,32)(34,44)(36,43)(42,45)(47,49);;
s3 := ( 3,10)( 4,19)( 5,31)( 6,12)( 7,28)( 8,27)( 9,38)(11,18)(13,37)(14,35)(15,32)(16,17)(20,29)(21,26)(22,42)(23,40)(24,49)(25,48)(30,34)(33,46)(36,45)(39,41)(43,50)(44,47);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2, 
s3*s1*s2*s3*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*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)!( 4, 5)( 6,19)( 7,21)( 9,30)(10,37)(11,31)(12,17)(13,28)(14,41)(15,27)(16,29)(22,40)(23,35)(24,46)(25,33)(26,32)(34,44)(36,43)(42,45)(47,49);
s3 := Sym(50)!( 3,10)( 4,19)( 5,31)( 6,12)( 7,28)( 8,27)( 9,38)(11,18)(13,37)(14,35)(15,32)(16,17)(20,29)(21,26)(22,42)(23,40)(24,49)(25,48)(30,34)(33,46)(36,45)(39,41)(43,50)(44,47);
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2, 
s3*s1*s2*s3*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2 >;