Part of the Atlas of Small Regular Polytopes

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

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

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