Part of the Atlas of Small Regular Polytopes

Polytope of Type {8,7}

Atlas Canonical Name {8,7}*1344

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1344,11291)
Rank
3
Schläfli Type
{8,7}
Vertices, edges, …
96, 336, 84
Order of s0s1s2
16
Order of s0s1s2s1
12
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

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)
s0 := ( 2, 7)( 3,19)( 4,31)( 5,22)( 6,30)( 8,27)( 9,28)(10,14)(12,13)(15,20)(16,24)(17,21)(23,25)(26,29);;
s1 := ( 1, 3)( 2,16)( 4,11)( 5,25)( 6,12)( 7,19)( 8,17)( 9,23)(10,15)(13,32)(14,29)(18,24)(20,28)(21,26)(22,27)(30,31);;
s2 := ( 1,32)( 2, 6)( 3,27)( 4,14)( 5,13)( 7,30)( 8,19)( 9,23)(10,31)(11,18)(12,22)(15,24)(16,20)(17,29)(21,26)(25,28);;
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*s1*s2*s1*s2*s1*s2*s1*s2, 
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, 
s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(32)!( 2, 7)( 3,19)( 4,31)( 5,22)( 6,30)( 8,27)( 9,28)(10,14)(12,13)(15,20)(16,24)(17,21)(23,25)(26,29);
s1 := Sym(32)!( 1, 3)( 2,16)( 4,11)( 5,25)( 6,12)( 7,19)( 8,17)( 9,23)(10,15)(13,32)(14,29)(18,24)(20,28)(21,26)(22,27)(30,31);
s2 := Sym(32)!( 1,32)( 2, 6)( 3,27)( 4,14)( 5,13)( 7,30)( 8,19)( 9,23)(10,31)(11,18)(12,22)(15,24)(16,20)(17,29)(21,26)(25,28);
poly := sub<Sym(32)|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*s1*s2*s1*s2*s1*s2*s1*s2, 
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, 
s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0 >; 

References

None.

to this polytope.

Twisty Puzzle