Part of the Atlas of Small Regular Polytopes

Polytope of Type {52,6}

Atlas Canonical Name {52,6}*624b

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(624,242)
Rank
3
Schläfli Type
{52,6}
Vertices, edges, …
52, 156, 6
Order of s0s1s2
39
Order of s0s1s2s1
4
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

13-fold

26-fold

Covers minimal covers in bold

2-fold

3-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP) 
s0 := ( 1, 3)( 2, 4)( 5,51)( 6,52)( 7,49)( 8,50)( 9,47)(10,48)(11,45)(12,46)(13,43)(14,44)(15,41)(16,42)(17,39)(18,40)(19,37)(20,38)(21,35)(22,36)(23,33)(24,34)(25,31)(26,32)(27,29)(28,30);;
s1 := ( 1, 5)( 2, 7)( 3, 6)( 4, 8)( 9,49)(10,51)(11,50)(12,52)(13,45)(14,47)(15,46)(16,48)(17,41)(18,43)(19,42)(20,44)(21,37)(22,39)(23,38)(24,40)(25,33)(26,35)(27,34)(28,36)(30,31);;
s2 := ( 2, 4)( 6, 8)(10,12)(14,16)(18,20)(22,24)(26,28)(30,32)(34,36)(38,40)(42,44)(46,48)(50,52);;
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, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(52)!( 1, 3)( 2, 4)( 5,51)( 6,52)( 7,49)( 8,50)( 9,47)(10,48)(11,45)(12,46)(13,43)(14,44)(15,41)(16,42)(17,39)(18,40)(19,37)(20,38)(21,35)(22,36)(23,33)(24,34)(25,31)(26,32)(27,29)(28,30);
s1 := Sym(52)!( 1, 5)( 2, 7)( 3, 6)( 4, 8)( 9,49)(10,51)(11,50)(12,52)(13,45)(14,47)(15,46)(16,48)(17,41)(18,43)(19,42)(20,44)(21,37)(22,39)(23,38)(24,40)(25,33)(26,35)(27,34)(28,36)(30,31);
s2 := Sym(52)!( 2, 4)( 6, 8)(10,12)(14,16)(18,20)(22,24)(26,28)(30,32)(34,36)(38,40)(42,44)(46,48)(50,52);
poly := sub<Sym(52)|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, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2 >;

References

None.

to this polytope.

Twisty Puzzle