Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,10}

Atlas Canonical Name {6,10}*960b

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(960,10891)
Rank
3
Schläfli Type
{6,10}
Vertices, edges, …
48, 240, 80
Order of s0s1s2
10
Order of s0s1s2s1
20
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

16-fold

120-fold

Covers minimal covers in bold

2-fold

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)^3> of order 2

60 facets

24 vertex figures

P/N, where N=<s0*(s1*s0*s2)^4*s1*s2> of order 2

40 facets

24 vertex figures

P/N, where N=<(s1*s2)^5> of order 2

40 facets

36 vertex figures

P/N, where N=<(s0*s1)^2> of order 3

32 facets

16 vertex figures

Representations

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

References

None.

to this polytope.

Twisty Puzzle