Part of the Atlas of Small Regular Polytopes

Polytope of Type {12,10}

Atlas Canonical Name {12,10}*960a

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(960,10870)
Rank
3
Schläfli Type
{12,10}
Vertices, edges, …
48, 240, 40
Order of s0s1s2
8
Order of s0s1s2s1
8
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

120-fold

Covers minimal covers in bold

2-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

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

References

None.

to this polytope.

Twisty Puzzle