Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,8,3}

Atlas Canonical Name {6,8,3}*1152

Overview

Group
SmallGroup(1152,155791)
Rank
4
Schläfli Type
{6,8,3}
Vertices, edges, …
6, 96, 48, 12
Order of s0s1s2s3
6
Order of s0s1s2s3s2s1
2
Also known as
{{6,8|2},{8,3}6}. if this polytope has another name.

Special Properties

  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

4-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)^4> of order 2

8 facets

6 vertex figures

  • 6 of 2-fold non-regular quotient of {8,3}*192
P/N, where N=<(s1*s2)^4, s1*s2*s3*(s2*s1)^3*s2*s3*s2> of order 4

4 facets

6 vertex figures

  • 6 of 4-fold non-regular quotient of {8,3}*192
P/N, where N=<(s1*s2)^2> of order 4

6 facets

6 vertex figures

  • 6 of 4-fold non-regular quotient of {8,3}*192

Representations

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

References

None.

to this polytope.