Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,5}

Atlas Canonical Name {3,5}*60

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Overview

Group
SmallGroup(60,5)
Rank
3
Schläfli Type
{3,5}
Vertices, edges, …
6, 15, 10
Order of s0s1s2
5
Order of s0s1s2s1
5
Also known as
hemiicosahedron, {3,5}5. if this polytope has another name.

Special Properties

  • Projective
  • Locally Spherical
  • Non-Orientable

Quotients maximal quotients in bold

No regular quotients.

Covers minimal covers in bold

2-fold

4-fold

6-fold

8-fold

10-fold

12-fold

14-fold

16-fold

18-fold

20-fold

22-fold

24-fold

26-fold

28-fold

30-fold

32-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

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

References

None.

to this polytope.

Twisty Puzzle