Part of the Atlas of Small Regular Polytopes

Polytope of Type {16,3}

Atlas Canonical Name {16,3}*768b

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(768,1085833)
Rank
3
Schläfli Type
{16,3}
Vertices, edges, …
128, 192, 24
Order of s0s1s2
6
Order of s0s1s2s1
16
Also known as
{16,3}6. if this polytope has another name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable

Quotients maximal quotients in bold

4-fold

16-fold

32-fold

64-fold

Covers minimal covers in bold

None in this atlas.

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)^8> of order 2

16 facets

64 vertex figures

P/N, where N=<(s0*s1)^3*s0*s2*(s1*s0)^6*s2*s1*s0> of order 2

12 facets

64 vertex figures

P/N, where N=<(s0*s1)^8, s0*s1*s2*(s1*s0)^5*s2*(s1*s0)^2*s1*s2> of order 4

8 facets

32 vertex figures

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

12 facets

32 vertex figures

P/N, where N=<s1*s2*(s1*s0)^3*s2*(s1*s0)^2*s1*s2, (s0*s1)^8> of order 4

8 facets

32 vertex figures

P/N, where N=<(s0*s1)^4, s1*s2*(s1*s0)^3*s2*(s1*s0)^2*s1*s2> of order 8

6 facets

16 vertex figures

P/N, where N=<s0*s1*s2*(s1*s0)^2*s2*s1, s1*s2*(s1*s0)^3*s2*(s1*s0)^2*s1*s2> of order 8

4 facets

16 vertex figures

P/N, where N=<s0*s1*s2*(s1*s0)^3*s1*s2*s1> of order 8

4 facets

16 vertex figures

P/N, where N=<(s0*s1)^2*s0*s2*(s1*s0)^3*s1*s2> of order 8

4 facets

16 vertex figures

P/N, where N=<(s0*s1)^4, s0*s1*s2*(s1*s0)^7*s1*s2*s1> of order 8

6 facets

16 vertex figures

P/N, where N=<(s0*s1)^2> of order 8

10 facets

16 vertex figures

Representations

Permutation Representation (GAP) 
s0 := ( 1,60)( 2,59)( 3,58)( 4,57)( 5,63)( 6,64)( 7,61)( 8,62)( 9,52)(10,51)(11,50)(12,49)(13,55)(14,56)(15,53)(16,54)(17,44)(18,43)(19,42)(20,41)(21,47)(22,48)(23,45)(24,46)(25,36)(26,35)(27,34)(28,33)(29,39)(30,40)(31,37)(32,38);;
s1 := ( 3, 4)( 5, 6)( 9,14)(10,13)(11,15)(12,16)(17,22)(18,21)(19,23)(20,24)(25,26)(31,32)(33,53)(34,54)(35,56)(36,55)(37,49)(38,50)(39,52)(40,51)(41,57)(42,58)(43,60)(44,59)(45,62)(46,61)(47,63)(48,64);;
s2 := ( 2, 3)( 5,10)( 6,12)( 7, 9)( 8,11)(13,16)(17,37)(18,39)(19,38)(20,40)(21,46)(22,48)(23,45)(24,47)(25,36)(26,34)(27,35)(28,33)(29,43)(30,41)(31,44)(32,42)(49,64)(50,62)(51,63)(52,61)(54,55)(58,59);;
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, 
s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(64)!( 1,60)( 2,59)( 3,58)( 4,57)( 5,63)( 6,64)( 7,61)( 8,62)( 9,52)(10,51)(11,50)(12,49)(13,55)(14,56)(15,53)(16,54)(17,44)(18,43)(19,42)(20,41)(21,47)(22,48)(23,45)(24,46)(25,36)(26,35)(27,34)(28,33)(29,39)(30,40)(31,37)(32,38);
s1 := Sym(64)!( 3, 4)( 5, 6)( 9,14)(10,13)(11,15)(12,16)(17,22)(18,21)(19,23)(20,24)(25,26)(31,32)(33,53)(34,54)(35,56)(36,55)(37,49)(38,50)(39,52)(40,51)(41,57)(42,58)(43,60)(44,59)(45,62)(46,61)(47,63)(48,64);
s2 := Sym(64)!( 2, 3)( 5,10)( 6,12)( 7, 9)( 8,11)(13,16)(17,37)(18,39)(19,38)(20,40)(21,46)(22,48)(23,45)(24,47)(25,36)(26,34)(27,35)(28,33)(29,43)(30,41)(31,44)(32,42)(49,64)(50,62)(51,63)(52,61)(54,55)(58,59);
poly := sub<Sym(64)|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, s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References

None.

to this polytope.

Twisty Puzzle