Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,2,12,8}

Atlas Canonical Name {3,2,12,8}*1152a

Overview

Group
SmallGroup(1152,97531)
Rank
5
Schläfli Type
{3,2,12,8}
Vertices, edges, …
3, 3, 12, 48, 8
Order of s0s1s2s3s4
24
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

3-fold

4-fold

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