From the emergence theory object library files…
A cluster of 4 regular tetrahedra, sharing one vertex, leaving small gaps between adjacent faces. By twisting each tetrahedron along an axis that goes through the sharing vertex and the centroid of the outer face, the gaps between the faces can be closed, while resulting in a pentagonal cone at the vertices. The twisting angle here is V3 and the resulting relative face angle is F3.
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: https://quantumgravityresearch.org/wp-content/uploads/2017/09/GF-paper-figures-w-description-SA-1.cdf
You can download the free Wolfram Mathematica file player here. https://www.wolfram.com/cdf-player/