Part of the Atlas of Small Regular Polytopes

Polytope of Type {8,4,6}

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

Overview

Group
SmallGroup(768,323566)
Rank
4
Schläfli Type
{8,4,6}
Vertices, edges, …
16, 32, 24, 6
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=<(s0*s1*s2*s1)^2> of order 2

6 facets

8 vertex figures

Representations

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

References

None.

to this polytope.