Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,12,2,2}

Atlas Canonical Name {6,12,2,2}*768b

Overview

Group
SmallGroup(768,1090163)
Rank
5
Schläfli Type
{6,12,2,2}
Vertices, edges, …
8, 48, 16, 2, 2
Order of s0s1s2s3s4
8
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

24-fold

Covers minimal covers in bold

None in this atlas.

Representations

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