Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {2,12,8,2}*768a

Overview

Group
SmallGroup(768,1035863)
Rank
5
Schläfli Type
{2,12,8,2}
Vertices, edges, …
2, 12, 48, 8, 2
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 := (1,2);;
s1 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(27,39)(28,41)(29,40)(30,42)(31,44)(32,43)(33,45)(34,47)(35,46)(36,48)(37,50)(38,49)(52,53)(55,56)(58,59)(61,62)(64,65)(67,68)(70,71)(73,74)(75,87)(76,89)(77,88)(78,90)(79,92)(80,91)(81,93)(82,95)(83,94)(84,96)(85,98)(86,97);;
s2 := ( 3,28)( 4,27)( 5,29)( 6,31)( 7,30)( 8,32)( 9,37)(10,36)(11,38)(12,34)(13,33)(14,35)(15,40)(16,39)(17,41)(18,43)(19,42)(20,44)(21,49)(22,48)(23,50)(24,46)(25,45)(26,47)(51,76)(52,75)(53,77)(54,79)(55,78)(56,80)(57,85)(58,84)(59,86)(60,82)(61,81)(62,83)(63,88)(64,87)(65,89)(66,91)(67,90)(68,92)(69,97)(70,96)(71,98)(72,94)(73,93)(74,95);;
s3 := ( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,60)(10,61)(11,62)(12,57)(13,58)(14,59)(15,63)(16,64)(17,65)(18,66)(19,67)(20,68)(21,72)(22,73)(23,74)(24,69)(25,70)(26,71)(27,81)(28,82)(29,83)(30,84)(31,85)(32,86)(33,75)(34,76)(35,77)(36,78)(37,79)(38,80)(39,93)(40,94)(41,95)(42,96)(43,97)(44,98)(45,87)(46,88)(47,89)(48,90)(49,91)(50,92);;
s4 := ( 99,100);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(100)!(1,2);
s1 := Sym(100)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(27,39)(28,41)(29,40)(30,42)(31,44)(32,43)(33,45)(34,47)(35,46)(36,48)(37,50)(38,49)(52,53)(55,56)(58,59)(61,62)(64,65)(67,68)(70,71)(73,74)(75,87)(76,89)(77,88)(78,90)(79,92)(80,91)(81,93)(82,95)(83,94)(84,96)(85,98)(86,97);
s2 := Sym(100)!( 3,28)( 4,27)( 5,29)( 6,31)( 7,30)( 8,32)( 9,37)(10,36)(11,38)(12,34)(13,33)(14,35)(15,40)(16,39)(17,41)(18,43)(19,42)(20,44)(21,49)(22,48)(23,50)(24,46)(25,45)(26,47)(51,76)(52,75)(53,77)(54,79)(55,78)(56,80)(57,85)(58,84)(59,86)(60,82)(61,81)(62,83)(63,88)(64,87)(65,89)(66,91)(67,90)(68,92)(69,97)(70,96)(71,98)(72,94)(73,93)(74,95);
s3 := Sym(100)!( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,60)(10,61)(11,62)(12,57)(13,58)(14,59)(15,63)(16,64)(17,65)(18,66)(19,67)(20,68)(21,72)(22,73)(23,74)(24,69)(25,70)(26,71)(27,81)(28,82)(29,83)(30,84)(31,85)(32,86)(33,75)(34,76)(35,77)(36,78)(37,79)(38,80)(39,93)(40,94)(41,95)(42,96)(43,97)(44,98)(45,87)(46,88)(47,89)(48,90)(49,91)(50,92);
s4 := Sym(100)!( 99,100);
poly := sub<Sym(100)|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*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;