This article was inspired by a conversation I had on the polytope discord server. (I'm the one who sent the message that links to.) I highly recommend joining this server if you like higher dimensional geometry. It's very mathematically dense, and they aren't the nicest if you ask a question sometimes, but it's good enough in my opinion. To get to this without using a browser, copy the link, press control+K in discord, paste in the link and hit enter. (Assuming you're in the polytope discord server.)

Symmetry

explain symmetry groups notice how under this definition of symmetry, a dodecahedron and icosidodecahedron are equally symmetrical explain transitivity and flag orbits talk about the discord conversation and how math terminology is super annoying sometimes

One type of symmetry is a symmetry group. A symmetry group dictates how an object doesn't change when transformed in specific ways. Symmetry groups are defined based off of mirror planes. Take for example B3, 3-cube symmetry. It has these 3 mirror planes, and if a polyhedron is symmetric when mirrored on these planes, it has B3 symmetry.