After I’d posted this, a helpful friend on Facebook told me the official name of the first polyhedron shown here — a pentalofted chamfered dodecahedron.
A Three-Level Dodecahedron, Together with Its Dual
RobertLovesPi.net
Polyhedra, tessellations, and more.
RobertLovesPi.net 
Wonderful Constructions and Colors——
On Wed, May 29, 2019 at 4:22 PM RobertLovesPi.net wrote:
> RobertLovesPi posted: ” I made these using Stella 4d, which you can try > for yourself, free, at http://www.software3d.com/Stella.php. ” >
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