Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,2,4,24}

Atlas Canonical Name {3,2,4,24}*1152d

Overview

Group
SmallGroup(1152,155800)
Rank
5
Schläfli Type
{3,2,4,24}
Vertices, edges, …
3, 3, 4, 48, 24
Order of s0s1s2s3s4
24
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 4,17)( 5,16)( 6,19)( 7,18)( 8,21)( 9,20)(10,23)(11,22)(12,25)(13,24)(14,27)(15,26)(28,41)(29,40)(30,43)(31,42)(32,45)(33,44)(34,47)(35,46)(36,49)(37,48)(38,51)(39,50)(52,65)(53,64)(54,67)(55,66)(56,69)(57,68)(58,71)(59,70)(60,73)(61,72)(62,75)(63,74)(76,89)(77,88)(78,91)(79,90)(80,93)(81,92)(82,95)(83,94)(84,97)(85,96)(86,99)(87,98);;
s3 := ( 5, 6)( 8,12)( 9,14)(10,13)(11,15)(17,18)(20,24)(21,26)(22,25)(23,27)(28,40)(29,42)(30,41)(31,43)(32,48)(33,50)(34,49)(35,51)(36,44)(37,46)(38,45)(39,47)(52,76)(53,78)(54,77)(55,79)(56,84)(57,86)(58,85)(59,87)(60,80)(61,82)(62,81)(63,83)(64,88)(65,90)(66,89)(67,91)(68,96)(69,98)(70,97)(71,99)(72,92)(73,94)(74,93)(75,95);;
s4 := ( 4,56)( 5,57)( 6,59)( 7,58)( 8,52)( 9,53)(10,55)(11,54)(12,60)(13,61)(14,63)(15,62)(16,68)(17,69)(18,71)(19,70)(20,64)(21,65)(22,67)(23,66)(24,72)(25,73)(26,75)(27,74)(28,92)(29,93)(30,95)(31,94)(32,88)(33,89)(34,91)(35,90)(36,96)(37,97)(38,99)(39,98)(40,80)(41,81)(42,83)(43,82)(44,76)(45,77)(46,79)(47,78)(48,84)(49,85)(50,87)(51,86);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3, 
s4*s3*s4*s3*s4*s3*s4*s3*s2*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(99)!(2,3);
s1 := Sym(99)!(1,2);
s2 := Sym(99)!( 4,17)( 5,16)( 6,19)( 7,18)( 8,21)( 9,20)(10,23)(11,22)(12,25)(13,24)(14,27)(15,26)(28,41)(29,40)(30,43)(31,42)(32,45)(33,44)(34,47)(35,46)(36,49)(37,48)(38,51)(39,50)(52,65)(53,64)(54,67)(55,66)(56,69)(57,68)(58,71)(59,70)(60,73)(61,72)(62,75)(63,74)(76,89)(77,88)(78,91)(79,90)(80,93)(81,92)(82,95)(83,94)(84,97)(85,96)(86,99)(87,98);
s3 := Sym(99)!( 5, 6)( 8,12)( 9,14)(10,13)(11,15)(17,18)(20,24)(21,26)(22,25)(23,27)(28,40)(29,42)(30,41)(31,43)(32,48)(33,50)(34,49)(35,51)(36,44)(37,46)(38,45)(39,47)(52,76)(53,78)(54,77)(55,79)(56,84)(57,86)(58,85)(59,87)(60,80)(61,82)(62,81)(63,83)(64,88)(65,90)(66,89)(67,91)(68,96)(69,98)(70,97)(71,99)(72,92)(73,94)(74,93)(75,95);
s4 := Sym(99)!( 4,56)( 5,57)( 6,59)( 7,58)( 8,52)( 9,53)(10,55)(11,54)(12,60)(13,61)(14,63)(15,62)(16,68)(17,69)(18,71)(19,70)(20,64)(21,65)(22,67)(23,66)(24,72)(25,73)(26,75)(27,74)(28,92)(29,93)(30,95)(31,94)(32,88)(33,89)(34,91)(35,90)(36,96)(37,97)(38,99)(39,98)(40,80)(41,81)(42,83)(43,82)(44,76)(45,77)(46,79)(47,78)(48,84)(49,85)(50,87)(51,86);
poly := sub<Sym(99)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3, 
s4*s3*s4*s3*s4*s3*s4*s3*s2*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s2*s3*s2 >;