Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,6,3}

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

Overview

Group
SmallGroup(1152,155791)
Rank
4
Schläfli Type
{6,6,3}
Vertices, edges, …
6, 96, 48, 16
Order of s0s1s2s3
24
Order of s0s1s2s3s2s1
2
Also known as
{{6,6|2},{6,3}8}. if this polytope has another name.

Special Properties

  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

4-fold

12-fold

24-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=<((s2*s1)^2*s2*s3)^2> of order 2

8 facets

6 vertex figures

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

4 facets

6 vertex figures

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

4 facets

6 vertex figures

  • 6 of 4-fold non-regular quotient of {6,3}*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 := ( 1,17)( 2,18)( 3,20)( 4,19)( 5,22)( 6,21)( 7,23)( 8,24)( 9,29)(10,30)(11,32)(12,31)(13,25)(14,26)(15,28)(16,27)(35,36)(37,38)(41,45)(42,46)(43,48)(44,47);;
s2 := ( 2, 4)( 5,15)( 6,14)( 7,13)( 8,16)( 9,11)(18,20)(21,31)(22,30)(23,29)(24,32)(25,27)(34,36)(37,47)(38,46)(39,45)(40,48)(41,43);;
s3 := ( 1, 7)( 2, 8)( 3, 6)( 4, 5)(11,12)(15,16)(17,23)(18,24)(19,22)(20,21)(27,28)(31,32)(33,39)(34,40)(35,38)(36,37)(43,44)(47,48);;
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, 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*s3*s2*s1*s3*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)!( 1,17)( 2,18)( 3,20)( 4,19)( 5,22)( 6,21)( 7,23)( 8,24)( 9,29)(10,30)(11,32)(12,31)(13,25)(14,26)(15,28)(16,27)(35,36)(37,38)(41,45)(42,46)(43,48)(44,47);
s2 := Sym(48)!( 2, 4)( 5,15)( 6,14)( 7,13)( 8,16)( 9,11)(18,20)(21,31)(22,30)(23,29)(24,32)(25,27)(34,36)(37,47)(38,46)(39,45)(40,48)(41,43);
s3 := Sym(48)!( 1, 7)( 2, 8)( 3, 6)( 4, 5)(11,12)(15,16)(17,23)(18,24)(19,22)(20,21)(27,28)(31,32)(33,39)(34,40)(35,38)(36,37)(43,44)(47,48);
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, 
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*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s2*s3*s2 >;

References

None.

to this polytope.