Hmm... can we be certain there is no convergent evolution at play? That certain families of triangles are descended from squares, but are so morphologically similar to those descended from circles they were left out of the data?
Back in the day I tried to explain the principles of phylogenetic reconstruction to undergraduates, using a selection of paper clips, bulldog clips and other sundry stationery items. I do not think my strategy was successful.
"Genetic analysis" done by a FRAUD!
Dr. Reuleaux has been exposed multiple times for his many conflicts of interest and a history of faking data! How his work here is still trusted even though NO ONE has ever verified it is beyond me...
Now this is going to be controversial, as: Plato et al; and Pulled et al; Nether et al; and Regions et al, all quite clearly show that that triangles are trapezoids which developed horns, most likely for defense.
Slightly related, I really enjoyed the book "Flatland" which explored the perspective of 2D a world that based social standing on number sides you had; and the explored traveling to a 1D world and entering the 3D.
It occurs to me I'm probably diving in here without ever having taken scuba lessons, BUT aren't parallelograms and trapezoids the knuckle draggers of Geometriphylogenetics?
Sometimes it is clear to me you are not funny, then I realize you are not funny in a very funny way and I snort what I'm drinking out of my nose which isn't funny, but the guy sitting in the next cubicle disagrees.
I love the idea that triangles are just the octopi of shapes. They took their own damn path down evolution and still got points.
Just like octopi took their own damn path down evolution and still got intelligent.