Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,2,4,12}

Atlas Canonical Name {3,2,4,12}*1152b

Overview

Group
SmallGroup(1152,157549)
Rank
5
Schläfli Type
{3,2,4,12}
Vertices, edges, …
3, 3, 8, 48, 24
Order of s0s1s2s3s4
12
Order of s0s1s2s3s4s3s2s1
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

None in this atlas.

Representations

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