Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,6,6}

Atlas Canonical Name {4,6,6}*768e

Overview

Group
SmallGroup(768,1089286)
Rank
4
Schläfli Type
{4,6,6}
Vertices, edges, …
4, 32, 48, 16
Order of s0s1s2s3
8
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

16-fold

24-fold

48-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<s1*(s2*s3)^2*s2*s1*s3> of order 2

8 facets

4 vertex figures

P/N, where N=<(s1*s2)^2> of order 3

8 facets

4 vertex figures

Representations

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

References

None.

to this polytope.