Part of the Atlas of Small Regular Polytopes

Polytope of Type {24,6,2}

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

Overview

Group
SmallGroup(1920,240809)
Rank
4
Schläfli Type
{24,6,2}
Vertices, edges, …
80, 240, 20, 2
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, 3)( 2,37)( 4,32)( 5,44)( 6,19)( 7,17)( 8,14)( 9,29)(10,20)(11,25)(12,31)(13,42)(15,47)(16,27)(18,38)(21,43)(22,45)(23,28)(24,34)(26,40)(30,48)(33,41)(35,36)(39,46);;
s1 := ( 1, 6)( 2,28)( 3,36)( 4,26)( 5,14)( 7,41)( 8,37)( 9,18)(10,11)(12,27)(13,48)(15,16)(17,25)(19,39)(20,47)(21,34)(22,33)(23,24)(29,43)(30,35)(31,44)(32,38)(40,42)(45,46);;
s2 := ( 1,27)( 2, 5)( 3,16)( 4, 9)( 6,35)( 7,10)( 8,13)(11,34)(12,48)(14,42)(17,20)(18,45)(19,36)(21,33)(22,38)(24,25)(29,32)(30,31)(37,44)(41,43);;
s3 := (49,50);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(50)!( 1, 3)( 2,37)( 4,32)( 5,44)( 6,19)( 7,17)( 8,14)( 9,29)(10,20)(11,25)(12,31)(13,42)(15,47)(16,27)(18,38)(21,43)(22,45)(23,28)(24,34)(26,40)(30,48)(33,41)(35,36)(39,46);
s1 := Sym(50)!( 1, 6)( 2,28)( 3,36)( 4,26)( 5,14)( 7,41)( 8,37)( 9,18)(10,11)(12,27)(13,48)(15,16)(17,25)(19,39)(20,47)(21,34)(22,33)(23,24)(29,43)(30,35)(31,44)(32,38)(40,42)(45,46);
s2 := Sym(50)!( 1,27)( 2, 5)( 3,16)( 4, 9)( 6,35)( 7,10)( 8,13)(11,34)(12,48)(14,42)(17,20)(18,45)(19,36)(21,33)(22,38)(24,25)(29,32)(30,31)(37,44)(41,43);
s3 := Sym(50)!(49,50);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2 >;