Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,4,12,2,5}

Atlas Canonical Name {2,4,12,2,5}*1920b

Overview

Group
SmallGroup(1920,240141)
Rank
6
Schläfli Type
{2,4,12,2,5}
Vertices, edges, …
2, 4, 24, 12, 5, 5
Order of s0s1s2s3s4s5
60
Order of s0s1s2s3s4s5s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

4-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := ( 3, 8)( 4,12)( 5,15)( 6,16)( 7,17)( 9,23)(10,24)(11,25)(13,29)(14,30)(18,35)(19,36)(20,34)(21,37)(22,38)(26,47)(27,45)(28,43)(31,44)(32,46)(33,42)(39,49)(40,50)(41,48);;
s2 := ( 4, 5)( 6, 7)( 8,18)(10,14)(11,13)(12,26)(15,31)(16,34)(17,19)(20,36)(21,22)(23,39)(24,42)(25,32)(27,30)(28,46)(29,43)(33,45)(37,48)(38,40)(41,50)(44,47);;
s3 := ( 3,11)( 4, 7)( 5,22)( 6,10)( 8,25)( 9,14)(12,17)(13,21)(15,38)(16,24)(18,28)(19,45)(20,31)(23,30)(26,41)(27,36)(29,37)(32,50)(33,39)(34,44)(35,43)(40,46)(42,49)(47,48);;
s4 := (52,53)(54,55);;
s5 := (51,52)(53,54);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*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, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s1*s2, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(55)!(1,2);
s1 := Sym(55)!( 3, 8)( 4,12)( 5,15)( 6,16)( 7,17)( 9,23)(10,24)(11,25)(13,29)(14,30)(18,35)(19,36)(20,34)(21,37)(22,38)(26,47)(27,45)(28,43)(31,44)(32,46)(33,42)(39,49)(40,50)(41,48);
s2 := Sym(55)!( 4, 5)( 6, 7)( 8,18)(10,14)(11,13)(12,26)(15,31)(16,34)(17,19)(20,36)(21,22)(23,39)(24,42)(25,32)(27,30)(28,46)(29,43)(33,45)(37,48)(38,40)(41,50)(44,47);
s3 := Sym(55)!( 3,11)( 4, 7)( 5,22)( 6,10)( 8,25)( 9,14)(12,17)(13,21)(15,38)(16,24)(18,28)(19,45)(20,31)(23,30)(26,41)(27,36)(29,37)(32,50)(33,39)(34,44)(35,43)(40,46)(42,49)(47,48);
s4 := Sym(55)!(52,53)(54,55);
s5 := Sym(55)!(51,52)(53,54);
poly := sub<Sym(55)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*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, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s1*s2, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;