Connect 20 Regular Octahedron units, get a Regular Icosahedron

[josdavi]

Please teach me how to prove that (as shown below):

 

Connect 20 Regular Octahedron (8-face solid) units together with exposing 4 faces per unit,

forming a ball-shape article, this article will enclose a Regular Icosahedron (20-face solid) inside.

 

Thank you.

[Captain Obvious]

While I can easily picture the 6 piece pole constructs, I cannot picture the 8 piece equatorial ring.

 

Am I being short sited? Or is an Octohedron required to have 60 and 120 degree sides?