Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,4,12}

Atlas Canonical Name {2,4,12}*384b

Overview

Group
SmallGroup(384,20049)
Rank
4
Schläfli Type
{2,4,12}
Vertices, edges, …
2, 8, 48, 24
Order of s0s1s2s3
12
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

12-fold

16-fold

24-fold

Covers minimal covers in bold

2-fold

3-fold

5-fold

Representations

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