Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,6,12}

Atlas Canonical Name {2,6,12}*1920b

Overview

Group
SmallGroup(1920,240977)
Rank
4
Schläfli Type
{2,6,12}
Vertices, edges, …
2, 40, 240, 80
Order of s0s1s2s3
6
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

120-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := ( 4,28)( 5,77)( 6,82)( 7,43)( 8,72)( 9,70)(10,45)(11,21)(12,15)(13,14)(17,66)(19,46)(20,49)(23,35)(24,41)(25,44)(26,80)(29,38)(30,81)(31,57)(32,55)(33,54)(34,56)(37,39)(40,78)(42,79)(47,50)(48,65)(51,64)(52,74)(53,61)(58,59)(62,69)(67,73)(68,71)(75,76);;
s2 := ( 4,24)( 5,23)( 6,39)( 7,82)( 8,50)( 9,46)(10,15)(11,13)(12,65)(14,71)(16,70)(17,66)(18,64)(19,63)(20,72)(21,49)(22,36)(25,42)(26,54)(28,34)(29,35)(30,78)(31,81)(32,44)(33,76)(38,41)(47,68)(51,73)(52,61)(53,59)(55,80)(56,77)(60,67)(75,79);;
s3 := ( 3,16)( 4,66)( 5,68)( 6,67)( 7,14)( 8,76)( 9,54)(10,37)(11,57)(12,56)(13,43)(15,34)(17,28)(18,27)(19,30)(20,29)(21,31)(22,63)(23,62)(24,61)(25,64)(26,65)(32,59)(33,70)(35,69)(36,60)(38,49)(39,45)(40,52)(41,53)(42,50)(44,51)(46,81)(47,79)(48,80)(55,58)(71,77)(72,75)(73,82)(74,78);;
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*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s3*s2*s1*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(82)!(1,2);
s1 := Sym(82)!( 4,28)( 5,77)( 6,82)( 7,43)( 8,72)( 9,70)(10,45)(11,21)(12,15)(13,14)(17,66)(19,46)(20,49)(23,35)(24,41)(25,44)(26,80)(29,38)(30,81)(31,57)(32,55)(33,54)(34,56)(37,39)(40,78)(42,79)(47,50)(48,65)(51,64)(52,74)(53,61)(58,59)(62,69)(67,73)(68,71)(75,76);
s2 := Sym(82)!( 4,24)( 5,23)( 6,39)( 7,82)( 8,50)( 9,46)(10,15)(11,13)(12,65)(14,71)(16,70)(17,66)(18,64)(19,63)(20,72)(21,49)(22,36)(25,42)(26,54)(28,34)(29,35)(30,78)(31,81)(32,44)(33,76)(38,41)(47,68)(51,73)(52,61)(53,59)(55,80)(56,77)(60,67)(75,79);
s3 := Sym(82)!( 3,16)( 4,66)( 5,68)( 6,67)( 7,14)( 8,76)( 9,54)(10,37)(11,57)(12,56)(13,43)(15,34)(17,28)(18,27)(19,30)(20,29)(21,31)(22,63)(23,62)(24,61)(25,64)(26,65)(32,59)(33,70)(35,69)(36,60)(38,49)(39,45)(40,52)(41,53)(42,50)(44,51)(46,81)(47,79)(48,80)(55,58)(71,77)(72,75)(73,82)(74,78);
poly := sub<Sym(82)|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*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s3*s2*s1*s3*s2 >;