Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,4,24}

Atlas Canonical Name {2,4,24}*384b

Overview

Group
SmallGroup(384,11274)
Rank
4
Schläfli Type
{2,4,24}
Vertices, edges, …
2, 4, 48, 24
Order of s0s1s2s3
24
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

3-fold

4-fold

6-fold

8-fold

12-fold

16-fold

24-fold

Covers minimal covers in bold

2-fold

3-fold

5-fold

Representations

Permutation Representation (GAP)
s0 := (1,2);;
s1 := ( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,58)(11,59)(12,60)(13,61)(14,62)(15,66)(16,67)(17,68)(18,63)(19,64)(20,65)(21,72)(22,73)(23,74)(24,69)(25,70)(26,71)(27,81)(28,82)(29,83)(30,84)(31,85)(32,86)(33,75)(34,76)(35,77)(36,78)(37,79)(38,80)(39,96)(40,97)(41,98)(42,93)(43,94)(44,95)(45,90)(46,91)(47,92)(48,87)(49,88)(50,89);;
s2 := ( 3,27)( 4,29)( 5,28)( 6,30)( 7,32)( 8,31)( 9,33)(10,35)(11,34)(12,36)(13,38)(14,37)(15,42)(16,44)(17,43)(18,39)(19,41)(20,40)(21,48)(22,50)(23,49)(24,45)(25,47)(26,46)(51,75)(52,77)(53,76)(54,78)(55,80)(56,79)(57,81)(58,83)(59,82)(60,84)(61,86)(62,85)(63,90)(64,92)(65,91)(66,87)(67,89)(68,88)(69,96)(70,98)(71,97)(72,93)(73,95)(74,94);;
s3 := ( 3, 4)( 6, 7)( 9,13)(10,12)(11,14)(15,19)(16,18)(17,20)(21,22)(24,25)(27,40)(28,39)(29,41)(30,43)(31,42)(32,44)(33,49)(34,48)(35,50)(36,46)(37,45)(38,47)(51,52)(54,55)(57,61)(58,60)(59,62)(63,67)(64,66)(65,68)(69,70)(72,73)(75,88)(76,87)(77,89)(78,91)(79,90)(80,92)(81,97)(82,96)(83,98)(84,94)(85,93)(86,95);;
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, s2*s3*s1*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s1*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(98)!(1,2);
s1 := Sym(98)!( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,58)(11,59)(12,60)(13,61)(14,62)(15,66)(16,67)(17,68)(18,63)(19,64)(20,65)(21,72)(22,73)(23,74)(24,69)(25,70)(26,71)(27,81)(28,82)(29,83)(30,84)(31,85)(32,86)(33,75)(34,76)(35,77)(36,78)(37,79)(38,80)(39,96)(40,97)(41,98)(42,93)(43,94)(44,95)(45,90)(46,91)(47,92)(48,87)(49,88)(50,89);
s2 := Sym(98)!( 3,27)( 4,29)( 5,28)( 6,30)( 7,32)( 8,31)( 9,33)(10,35)(11,34)(12,36)(13,38)(14,37)(15,42)(16,44)(17,43)(18,39)(19,41)(20,40)(21,48)(22,50)(23,49)(24,45)(25,47)(26,46)(51,75)(52,77)(53,76)(54,78)(55,80)(56,79)(57,81)(58,83)(59,82)(60,84)(61,86)(62,85)(63,90)(64,92)(65,91)(66,87)(67,89)(68,88)(69,96)(70,98)(71,97)(72,93)(73,95)(74,94);
s3 := Sym(98)!( 3, 4)( 6, 7)( 9,13)(10,12)(11,14)(15,19)(16,18)(17,20)(21,22)(24,25)(27,40)(28,39)(29,41)(30,43)(31,42)(32,44)(33,49)(34,48)(35,50)(36,46)(37,45)(38,47)(51,52)(54,55)(57,61)(58,60)(59,62)(63,67)(64,66)(65,68)(69,70)(72,73)(75,88)(76,87)(77,89)(78,91)(79,90)(80,92)(81,97)(82,96)(83,98)(84,94)(85,93)(86,95);
poly := sub<Sym(98)|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, 
s2*s3*s1*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s1*s3*s2*s3 >;