Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1152,157549)
Rank
5
Schläfli Type
{3,2,12,4}
Vertices, edges, …
3, 3, 24, 48, 8
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 := ( 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);;
s3 := ( 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);;
s4 := ( 4,55)( 5,54)( 6,53)( 7,52)( 8,59)( 9,58)(10,57)(11,56)(12,63)(13,62)(14,61)(15,60)(16,67)(17,66)(18,65)(19,64)(20,71)(21,70)(22,69)(23,68)(24,75)(25,74)(26,73)(27,72)(28,79)(29,78)(30,77)(31,76)(32,83)(33,82)(34,81)(35,80)(36,87)(37,86)(38,85)(39,84)(40,91)(41,90)(42,89)(43,88)(44,95)(45,94)(46,93)(47,92)(48,99)(49,98)(50,97)(51,96);;
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, s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*s3, 
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(99)!(2,3);
s1 := Sym(99)!(1,2);
s2 := 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);
s3 := 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);
s4 := Sym(99)!( 4,55)( 5,54)( 6,53)( 7,52)( 8,59)( 9,58)(10,57)(11,56)(12,63)(13,62)(14,61)(15,60)(16,67)(17,66)(18,65)(19,64)(20,71)(21,70)(22,69)(23,68)(24,75)(25,74)(26,73)(27,72)(28,79)(29,78)(30,77)(31,76)(32,83)(33,82)(34,81)(35,80)(36,87)(37,86)(38,85)(39,84)(40,91)(41,90)(42,89)(43,88)(44,95)(45,94)(46,93)(47,92)(48,99)(49,98)(50,97)(51,96);
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, 
s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;