I could be wrong, but... here goes.
The Mortarboard is square. 90 degrees on each side. = 360
High School, Undergrad degrees, Masters degrees fall under this.
The tassel sits one side representing 90 degrees of knowledge
The Tam is an octagon. They're 135 degrees at each angle, 1080 degrees internally and 360 degrees externally,
Doctorate degrees fall under this. the Tassel sits on 135 degrees
that's about a 1 4th of 360 degrees.
The Fez - Is a cylinder with a circular top, Circles are 360 degrees
which in "full circle" represent great knowledge by the wearer identifying them as a noble aristocrat. Where the tassel is pinned to hang represents a specific degree of knowledge, If its not pinned down, represents 360 in total.
On fiction they typically put the Fez on monkey's, mocking black men, who dawned them in real life/, they're also put on also genies, or wise men.
Phrygian cap is a like a oblique cone, i with a pointed apex. thy vary is volume and radius. There are no tassels. It represent the free man (Free Black People) Those set free by the Romans who once enslaved them ..It's also called the Liberty Cap.
In Fiction you see it worn by:
Link from Legend of Zelda: Power Wisdom and Courage.
Santa Claus: Happiness and the greater good
Then there are elves, dwarfs, pygmy's gnomes, smurfs who have great power, great wisdom in their stories
In real life: Atop the US Capital building is the Statue of Freedom (The Roman Goddess "Libertas")
The statue was supposed to dawn the liberty cap, but the confederate president Jefferson Davis did not approve of the Liberty Cap.being in the final creation of the statue stating these words
"American liberty is original and not the liberty of the freed slave"
The more you know.