Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,10}

Atlas Canonical Name {4,10}*960

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Overview

Group
SmallGroup(960,10882)
Rank
3
Schläfli Type
{4,10}
Vertices, edges, …
48, 240, 120
Order of s0s1s2
12
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

60-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)^2*s2*s1*s0*(s2*s1)^3*s0*s2*s1*s2> of order 2

60 facets

24 vertex figures

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

60 facets

36 vertex figures

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

60 facets

24 vertex figures

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

64 facets

24 vertex figures

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

40 facets

16 vertex figures

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

30 facets

12 vertex figures

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

34 facets

12 vertex figures

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

32 facets

18 vertex figures

P/N, where N=<s2*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 5

24 facets

16 vertex figures

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

20 facets

8 vertex figures

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

24 facets

8 vertex figures

P/N, where N=<(s1*s2)^2, (s0*s1)^2*s2*s1*s0*(s2*s1)^3*s0> of order 10

12 facets

8 vertex figures

P/N, where N=<(s0*s1)^2, s2*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 10

16 facets

8 vertex figures

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

10 facets

4 vertex figures

Representations

Permutation Representation (GAP) 
s0 := (3,4)(7,8);;
s1 := (1,3)(2,4)(6,7)(8,9);;
s2 := ( 5, 6)( 7, 8)(10,11);;
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, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(11)!(3,4)(7,8);
s1 := Sym(11)!(1,3)(2,4)(6,7)(8,9);
s2 := Sym(11)!( 5, 6)( 7, 8)(10,11);
poly := sub<Sym(11)|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, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1 >;

References

None.

to this polytope.

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