Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,28}

Atlas Canonical Name {6,28}*1344c

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1344,11291)
Rank
3
Schläfli Type
{6,28}
Vertices, edges, …
24, 336, 112
Order of s0s1s2
7
Order of s0s1s2s1
16
Also known as
if this polytope has a name.

Special Properties

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

References

None.

to this polytope.

Twisty Puzzle