Wow! I’d totally forgotten PB was the IQ (Inigo Quilez) of a different generation.. What a blast from the past, and learnt so much from this site 20+ years ago!
Can such a honeycomb be made of the chiral aperiodic monotile ("spectre"), which is closely related to a hexagon?
I could have sworn the "order 5 cubic honeycomb" image was a direct screencap of Beyond the Mind's Eye.