Part of the Atlas of Small Regular Polytopes

Polytope of Type {24,4}

Atlas Canonical Name {24,4}*960a

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(960,5719)
Rank
3
Schläfli Type
{24,4}
Vertices, edges, …
120, 240, 20
Order of s0s1s2
20
Order of s0s1s2s1
6
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

Irregular Quotients of which this is a minimal cover

None.

Representations

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

References

None.

to this polytope.

Twisty Puzzle