Fascinating stuff. I've often thought that the nature of hallucinations - geometric or otherwise - must have lots to tell us about the workings of the brain. From a mechanistic viewpoint all our experiences (hallucinations included) supervene on brain structure, therefore these common geometric hallucinations likely reflect some fundamental structure of the brain.
"But it's not just hallucinogenic drugs like LSD, cannabis or mescaline that conjure up these geometric structures."
The article seems to be interesting, but this start turned me off a bit, as it is wrong. Cannabis is not hallucinogenic. When you get hallucinations from cannabis, then you might have a problem called psychosis...
https://news.ycombinator.com/item?id=10397619