Part of the Atlas of Small Regular Polytopes

Polytope of Type {5,12,2}

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

Overview

Group
SmallGroup(960,10889)
Rank
4
Schläfli Type
{5,12,2}
Vertices, edges, …
20, 120, 48, 2
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 := ( 2,10)( 3,12)( 4,17)( 5,19)( 7,38)(11,28)(13,44)(14,43)(15,34)(20,23)(21,36)(22,37)(24,26)(29,33)(30,31)(32,35)(39,47)(40,46)(41,45)(42,48);;
s1 := ( 2, 3)( 4,17)( 5,19)( 7,28)( 8,35)( 9,29)(10,15)(11,26)(12,39)(13,25)(14,27)(20,38)(21,33)(22,44)(23,31)(24,30)(32,42)(34,41)(40,43)(45,47);;
s2 := ( 1, 8)( 2,17)( 3,29)( 4,10)( 5,26)( 6,25)( 7,36)( 9,16)(11,35)(12,33)(13,30)(14,15)(18,27)(19,24)(20,40)(21,38)(22,47)(23,46)(28,32)(31,44)(34,43)(37,39)(41,48)(42,45);;
s3 := (49,50);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(50)!( 2,10)( 3,12)( 4,17)( 5,19)( 7,38)(11,28)(13,44)(14,43)(15,34)(20,23)(21,36)(22,37)(24,26)(29,33)(30,31)(32,35)(39,47)(40,46)(41,45)(42,48);
s1 := Sym(50)!( 2, 3)( 4,17)( 5,19)( 7,28)( 8,35)( 9,29)(10,15)(11,26)(12,39)(13,25)(14,27)(20,38)(21,33)(22,44)(23,31)(24,30)(32,42)(34,41)(40,43)(45,47);
s2 := Sym(50)!( 1, 8)( 2,17)( 3,29)( 4,10)( 5,26)( 6,25)( 7,36)( 9,16)(11,35)(12,33)(13,30)(14,15)(18,27)(19,24)(20,40)(21,38)(22,47)(23,46)(28,32)(31,44)(34,43)(37,39)(41,48)(42,45);
s3 := Sym(50)!(49,50);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 >;