Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,24,6}

Atlas Canonical Name {2,24,6}*1920d

Overview

Group
SmallGroup(1920,240809)
Rank
4
Schläfli Type
{2,24,6}
Vertices, edges, …
2, 80, 240, 20
Order of s0s1s2s3
24
Order of s0s1s2s3s2s1
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

8-fold

Covers minimal covers in bold

None in this atlas.

Representations

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