Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,24,2}

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

Overview

Group
SmallGroup(384,11274)
Rank
4
Schläfli Type
{4,24,2}
Vertices, edges, …
4, 48, 24, 2
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 := ( 1,49)( 2,50)( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,58)(11,59)(12,60)(13,64)(14,65)(15,66)(16,61)(17,62)(18,63)(19,70)(20,71)(21,72)(22,67)(23,68)(24,69)(25,79)(26,80)(27,81)(28,82)(29,83)(30,84)(31,73)(32,74)(33,75)(34,76)(35,77)(36,78)(37,94)(38,95)(39,96)(40,91)(41,92)(42,93)(43,88)(44,89)(45,90)(46,85)(47,86)(48,87);;
s1 := ( 1,25)( 2,27)( 3,26)( 4,28)( 5,30)( 6,29)( 7,31)( 8,33)( 9,32)(10,34)(11,36)(12,35)(13,40)(14,42)(15,41)(16,37)(17,39)(18,38)(19,46)(20,48)(21,47)(22,43)(23,45)(24,44)(49,73)(50,75)(51,74)(52,76)(53,78)(54,77)(55,79)(56,81)(57,80)(58,82)(59,84)(60,83)(61,88)(62,90)(63,89)(64,85)(65,87)(66,86)(67,94)(68,96)(69,95)(70,91)(71,93)(72,92);;
s2 := ( 1, 2)( 4, 5)( 7,11)( 8,10)( 9,12)(13,17)(14,16)(15,18)(19,20)(22,23)(25,38)(26,37)(27,39)(28,41)(29,40)(30,42)(31,47)(32,46)(33,48)(34,44)(35,43)(36,45)(49,50)(52,53)(55,59)(56,58)(57,60)(61,65)(62,64)(63,66)(67,68)(70,71)(73,86)(74,85)(75,87)(76,89)(77,88)(78,90)(79,95)(80,94)(81,96)(82,92)(83,91)(84,93);;
s3 := (97,98);;
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*s0*s1*s0*s1*s0*s1, s1*s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s0*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(98)!( 1,49)( 2,50)( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,58)(11,59)(12,60)(13,64)(14,65)(15,66)(16,61)(17,62)(18,63)(19,70)(20,71)(21,72)(22,67)(23,68)(24,69)(25,79)(26,80)(27,81)(28,82)(29,83)(30,84)(31,73)(32,74)(33,75)(34,76)(35,77)(36,78)(37,94)(38,95)(39,96)(40,91)(41,92)(42,93)(43,88)(44,89)(45,90)(46,85)(47,86)(48,87);
s1 := Sym(98)!( 1,25)( 2,27)( 3,26)( 4,28)( 5,30)( 6,29)( 7,31)( 8,33)( 9,32)(10,34)(11,36)(12,35)(13,40)(14,42)(15,41)(16,37)(17,39)(18,38)(19,46)(20,48)(21,47)(22,43)(23,45)(24,44)(49,73)(50,75)(51,74)(52,76)(53,78)(54,77)(55,79)(56,81)(57,80)(58,82)(59,84)(60,83)(61,88)(62,90)(63,89)(64,85)(65,87)(66,86)(67,94)(68,96)(69,95)(70,91)(71,93)(72,92);
s2 := Sym(98)!( 1, 2)( 4, 5)( 7,11)( 8,10)( 9,12)(13,17)(14,16)(15,18)(19,20)(22,23)(25,38)(26,37)(27,39)(28,41)(29,40)(30,42)(31,47)(32,46)(33,48)(34,44)(35,43)(36,45)(49,50)(52,53)(55,59)(56,58)(57,60)(61,65)(62,64)(63,66)(67,68)(70,71)(73,86)(74,85)(75,87)(76,89)(77,88)(78,90)(79,95)(80,94)(81,96)(82,92)(83,91)(84,93);
s3 := Sym(98)!(97,98);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s0*s2*s1*s2 >;