Part of the Atlas of Small Regular Polytopes

Polytope of Type {8,3}

Atlas Canonical Name {8,3}*96

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Overview

Group
SmallGroup(96,193)
Rank
3
Schläfli Type
{8,3}
Vertices, edges, …
16, 24, 6
Order of s0s1s2
12
Order of s0s1s2s1
8
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

7-fold

8-fold

9-fold

10-fold

11-fold

12-fold

13-fold

14-fold

15-fold

17-fold

18-fold

19-fold

20-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

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

References

None.

to this polytope.

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