Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,24,2}

Atlas Canonical Name {6,24,2}*1152a

Overview

Group
SmallGroup(1152,155485)
Rank
4
Schläfli Type
{6,24,2}
Vertices, edges, …
12, 144, 48, 2
Order of s0s1s2s3
6
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

3-fold

4-fold

12-fold

24-fold

Covers minimal covers in bold

None in this atlas.

Representations

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