Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,4,24}

Atlas Canonical Name {2,4,24}*768d

Overview

Group
SmallGroup(768,1089137)
Rank
4
Schläfli Type
{2,4,24}
Vertices, edges, …
2, 8, 96, 48
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

4-fold

8-fold

16-fold

24-fold

32-fold

48-fold

Covers minimal covers in bold

None in this atlas.

Representations

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