Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,12,3,2,5}

Atlas Canonical Name {2,12,3,2,5}*1920

Overview

Group
SmallGroup(1920,240195)
Rank
6
Schläfli Type
{2,12,3,2,5}
Vertices, edges, …
2, 16, 24, 4, 5, 5
Order of s0s1s2s3s4s5
40
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 := ( 4, 5)( 6, 7)( 8,21)( 9,24)(11,16)(12,15)(13,33)(14,36)(17,39)(18,40)(19,25)(20,22)(23,44)(26,43)(27,28)(29,45)(30,47)(31,34)(32,37)(35,49)(38,50)(41,42);;
s2 := ( 3,11)( 4, 6)( 5,27)( 7,12)( 8,50)( 9,49)(10,15)(13,44)(14,43)(16,28)(17,48)(18,46)(19,38)(20,35)(21,34)(22,36)(23,32)(24,37)(25,33)(26,31)(29,42)(30,41)(39,45)(40,47);;
s3 := ( 3,48)( 4,42)( 5,41)( 6,38)( 7,50)( 8,13)( 9,14)(10,46)(11,26)(12,44)(15,23)(16,43)(17,31)(18,32)(19,29)(20,30)(21,33)(22,47)(24,36)(25,45)(27,35)(28,49)(34,39)(37,40);;
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, 
s2*s3*s2*s3*s2*s3, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, 
s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(55)!(1,2);
s1 := Sym(55)!( 4, 5)( 6, 7)( 8,21)( 9,24)(11,16)(12,15)(13,33)(14,36)(17,39)(18,40)(19,25)(20,22)(23,44)(26,43)(27,28)(29,45)(30,47)(31,34)(32,37)(35,49)(38,50)(41,42);
s2 := Sym(55)!( 3,11)( 4, 6)( 5,27)( 7,12)( 8,50)( 9,49)(10,15)(13,44)(14,43)(16,28)(17,48)(18,46)(19,38)(20,35)(21,34)(22,36)(23,32)(24,37)(25,33)(26,31)(29,42)(30,41)(39,45)(40,47);
s3 := Sym(55)!( 3,48)( 4,42)( 5,41)( 6,38)( 7,50)( 8,13)( 9,14)(10,46)(11,26)(12,44)(15,23)(16,43)(17,31)(18,32)(19,29)(20,30)(21,33)(22,47)(24,36)(25,45)(27,35)(28,49)(34,39)(37,40);
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, s2*s3*s2*s3*s2*s3, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, 
s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3*s1*s2 >;