From the emergence theory object library files…
 
Overlaying vertex-sharing 3-fold cluster (blue) and vertex-sharing 5-fold cluster (yellow) together. Notice that the vertex-sharing 3-fold cluster is embedded in the vertex sharing 5-fold cluster with the same handedness.
 
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/