Shape carved out by all 12 pentagonal pyramids in an icosahedron?

[repoman]

Similar to making another internal regular hexagon by connecting all non adjacent and non opposite corners.

Talking about internal pyramids which are taller than the 12 pyramids on the surface.

For the 12 pentagon bases I think the all of the together will make a regular dodecahedron. But what about the solid carved out from the 5×12 = 60 isosceles triangles of the pyramids minus the bases?

 

[fromderinside]

Let's give the Babylonians a call .... After all they made Daniel and  Shadrach Meshach and Abednego. Seems they believed in counting knuckles. There are 60 yano. Maybe nothing to do with geometry just anatomy, algebra and business.