Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,6,3}

Atlas Canonical Name {4,6,3}*1152a

Overview

Group
SmallGroup(1152,155790)
Rank
4
Schläfli Type
{4,6,3}
Vertices, edges, …
8, 96, 72, 12
Order of s0s1s2s3
12
Order of s0s1s2s3s2s1
4
Also known as
if this polytope has a name.

Special Properties

  • Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

4-fold

6-fold

12-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=<(s0*s1)^2> of order 2

12 facets

  • 12 of 2-fold non-regular quotient of {4,6}*96

4 vertex figures

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

8 facets

8 vertex figures

  • 8 of 2-fold non-regular quotient of {6,3}*144
P/N, where N=<(s0*s1)^2, (s1*s2)^3> of order 4

8 facets

  • 4 of 2-fold non-regular quotient of {4,3}*48
  • 4 of 2-fold non-regular quotient of {4,6}*96

4 vertex figures

  • 4 of 2-fold non-regular quotient of {6,3}*144
P/N, where N=<(s0*s1)^2, s1*s2*s1*s3*(s2*s1)^2*s3*s2> of order 4

6 facets

  • 6 of 2-fold non-regular quotient of {4,6}*96

4 vertex figures

  • 4 of 2-fold non-regular quotient of {6,3}*144

Representations

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

References

None.

to this polytope.