Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,2,3,12,3}

Atlas Canonical Name {2,2,3,12,3}*1920

Overview

Group
SmallGroup(1920,240973)
Rank
6
Schläfli Type
{2,2,3,12,3}
Vertices, edges, …
2, 2, 5, 40, 40, 5
Order of s0s1s2s3s4s5
10
Order of s0s1s2s3s4s5s4s3s2s1
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

Covers minimal covers in bold

None in this atlas.

Representations

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