I have been playing with rotating an ellipse at speed 1,
while moving a point around the ellipse at a different speed s. The
dimensions of the ellipse are 1 by d.
It gives fun spiral graph pictures.

The pentacle and triangle with almost straight edges surprised me.
An n (odd) pointed one is made with d=n-1 and s= -(n-1).
But the second row shows s=-6 with more and more skinny ellipses.
The first has convex lines and the last concave, so there has to be a
place in the middle.

The shifted circle with d=4 and s=2 is also fun.

Of course the bottom right was given thickness by adding an small shift to s.

The 3rd was a mistake.

The trials of not being busy teaching. <3

wolframalpha

parametric plot [[0,1],[1,0]]*[[cos(t),-sin(t)],[sin(t),cos(t)]]*[[4,0],[0,1]]*[[cos(t),sin(t)],[-sin(t),cos(t)]]*[cos(-4*t),sin(-4*t)]

[cos(-4*t),sin(-4*t)] moves the point around a circle at speed s=-4.

[[cos(t),sin(t)],[-sin(t),cos(t)]] rotates this point by an angle of
t.

[[4,0],[0,1]] stretches it in the x direction by d=4.

[[cos(t),-sin(t)],[sin(t),cos(t)]] rotates it back the angle of t.

[[0,1],[1,0]] rotate the peak to the top.

"parametric plot" plots it for values of t.