Is there a name for these shapes? Polygons with rounded corners made with polar coordinates

I've heard the four-sided versions be called squircles (square circles).

roundygons?

edit: fun fact, these shapes are the EXACT toolpaths cutting tools take when CNC machines move spinning cutters through the material. if the radii are chosen with regard to the tool size, the resulting shape can have sharp corners or rounded corners.
Would have been nice if you included some neatly written formulae and plotted graphs. I have previously made polar representations of squares and rectangles with rounded corners, but their formulae were different than yours (yours seem simpler). And no, I don’t think they have special names for such shapes.
They look similar to Lamé curves.

Despite their name, the Lamé curves aren't lame.
Obviously the nobel prize part is a joke, but it would be a fields medal probably! Math isnt a field the nobel prize is awarded in
I belive those are called "badly drawen circles"
You can't get a nobel prize in math.  It's literally the only subject that is exempt.  IIRC, it's cause Nobel had a math teacher he didn't like.

So you'll have to get a fields medal case instead, sorry.

Edit: correction: actually there are lots of fields that cant get a nobel prize.

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