(Basic Geometry) What is a geometric object that is universally inverse symmetric about a point called?

Question

I may be explaining this wrong, but hopefully, an example will make things clear. Take a look at this figure where every black line that passes through the blue dot separates the original red traced shape into two "inversely" symmetric sub-traces that each has the same area (and are essentially just flipped images of each other):

Is there a geometric term to describe shapes like these?

Thanks

Answer 1

That's centrally symmetric. (Attested in https://en.wikipedia.org/wiki/Point_reflection)

(In two dimensions, it happens to be the same as $180^{\circ}$ rotational symmetry, but in higher dimensions, these concepts are different.)

Edit: Oh I almost forgot, a stronger notion is a balanced set. A set is balanced if and only if it is both centrally symmetric and star convex (around the same point). In your example, it looks like the inside of the red curve is balanced.