Part of the Atlas of Small Regular Polytopes

Polytope of Type {15,3}

Atlas Canonical Name {15,3}*1440

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Overview

Group
SmallGroup(1440,5848)
Rank
3
Schläfli Type
{15,3}
Vertices, edges, …
240, 360, 48
Order of s0s1s2
20
Order of s0s1s2s1
15
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable

Quotients maximal quotients in bold

4-fold

12-fold

24-fold

60-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)^5*s0*s2*(s1*s0)^4*s1*s2> of order 2

24 facets

120 vertex figures

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

24 facets

120 vertex figures

P/N, where N=<(s1*s0)^2*s2*(s1*s0)^7*s2*s1*s0*s1*s2> of order 2

24 facets

120 vertex figures

P/N, where N=<(s0*s1)^5> of order 3

24 facets

80 vertex figures

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

16 facets

80 vertex figures

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

12 facets

60 vertex figures

P/N, where N=<s0*s1*s0*(s2*(s1*s0)^3)^2*s2*s1*s0*s1, (s0*s1)^5*s0*s2*(s1*s0)^4*s1*s2> of order 4

12 facets

60 vertex figures

P/N, where N=<(s0*s1)^3*s0*s2*(s1*s0)^3*s2*(s1*s0)^2*s1, (s1*s0)^4*s2*(s1*s0)^5*s1*s2*s1> of order 4

12 facets

60 vertex figures

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

16 facets

48 vertex figures

P/N, where N=<(s0*s1)^5, s0*s1*s2*(s1*s0)^4*s2*(s1*s0)^3*s2*s1*s0*s1*s2> of order 6

12 facets

40 vertex figures

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

8 facets

40 vertex figures

P/N, where N=<(s0*s1)^3, s0*s1*s2*(s1*s0)^7*s2*s1*s0*s1*s2> of order 10

8 facets

24 vertex figures

P/N, where N=<(s0*s1)^2*s0*s2*(s1*s0)^3*s2*s1, s0*s1*s0*s2*(s1*s0)^3*s2*s1*s0*s1> of order 12

4 facets

20 vertex figures

Representations

Permutation Representation (GAP) 
s0 := (2,3)(4,5)(7,9);;
s1 := (1,2)(3,4)(8,9);;
s2 := (2,5)(3,4)(6,8);;
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*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*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 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(9)!(2,3)(4,5)(7,9);
s1 := Sym(9)!(1,2)(3,4)(8,9);
s2 := Sym(9)!(2,5)(3,4)(6,8);
poly := sub<Sym(9)|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*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*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 >;

References

None.

to this polytope.

Twisty Puzzle