From the emergence theory object library files…
A cluster of 5 regular tetrahedra, sharing one edge, leaving small gaps between adjacent faces. By twisting each tetrahedron along an axis that goes through the mid-point of the sharing edge and the mid-point of the outer edge, the gaps between the faces can be closed, while resulting in a pentagonal cone at the vertices. The twisting angle here is E5 and the resulting relative face angle is F5.
In this video we are rotating the structure around in Mathematica, viewing it from various angles, and changing the rotation angle as well as the transparency of the tetrahedra.
To rotate and manipulate this object yourself, you can download the Mathematica file associated with this object here:
You can download the free Wolfram Mathematica file player here.