Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,8,4}

Atlas Canonical Name {6,8,4}*768b

Overview

Group
SmallGroup(768,323566)
Rank
4
Schläfli Type
{6,8,4}
Vertices, edges, …
6, 48, 32, 8
Order of s0s1s2s3
12
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

3-fold

4-fold

6-fold

8-fold

12-fold

16-fold

24-fold

32-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*s2)^2> of order 2

4 facets

6 vertex figures

Representations

Permutation Representation (GAP) 
s0 := ( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)(35,36)(38,39)(41,42)(44,45)(47,48);;
s1 := ( 1,27)( 2,26)( 3,25)( 4,30)( 5,29)( 6,28)( 7,33)( 8,32)( 9,31)(10,36)(11,35)(12,34)(13,48)(14,47)(15,46)(16,45)(17,44)(18,43)(19,42)(20,41)(21,40)(22,39)(23,38)(24,37);;
s2 := ( 7,10)( 8,11)( 9,12)(19,22)(20,23)(21,24)(25,37)(26,38)(27,39)(28,40)(29,41)(30,42)(31,46)(32,47)(33,48)(34,43)(35,44)(36,45);;
s3 := (13,22)(14,23)(15,24)(16,19)(17,20)(18,21)(37,46)(38,47)(39,48)(40,43)(41,44)(42,45);;
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*s2*s1*s0*s1*s2*s1, 
s2*s3*s2*s3*s2*s3*s2*s3, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(48)!( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)(35,36)(38,39)(41,42)(44,45)(47,48);
s1 := Sym(48)!( 1,27)( 2,26)( 3,25)( 4,30)( 5,29)( 6,28)( 7,33)( 8,32)( 9,31)(10,36)(11,35)(12,34)(13,48)(14,47)(15,46)(16,45)(17,44)(18,43)(19,42)(20,41)(21,40)(22,39)(23,38)(24,37);
s2 := Sym(48)!( 7,10)( 8,11)( 9,12)(19,22)(20,23)(21,24)(25,37)(26,38)(27,39)(28,40)(29,41)(30,42)(31,46)(32,47)(33,48)(34,43)(35,44)(36,45);
s3 := Sym(48)!(13,22)(14,23)(15,24)(16,19)(17,20)(18,21)(37,46)(38,47)(39,48)(40,43)(41,44)(42,45);
poly := sub<Sym(48)|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*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2 >;

References

None.

to this polytope.