Part of the Atlas of Small Regular Polytopes

Polytope of Type {24,4,2}

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

Overview

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