Opposite of Polygon: Open Shapes & Names

[aspiring_one]

Sorry if this seems elementary but what shapes are the opposite of polygons (closed by line segments) and what do you call them? Sorry if my question is phrased weird.

 

[disregardthat]

What do you mean by the opposite of a geometrical figure?

 

[aspiring_one]

I guess I mean curved shapes that end in points. Not quite conics but a combination of them. One shape is a diamond with curved edges inward. I am no geometer nor have I taken any topology. Sorry if this is still vague

 

[chiro]

Sorry if this seems elementary but what shapes are the opposite of polygons (closed by line segments) and what do you call them? Sorry if my question is phrased weird.

If I had to guess, I would have to see anything that has curves. If I had to define curve, I would define an object with a boundary that at all points has a changing derivative: in other words no straight lines on the objects boundary which means that the derivative is non-constant about any local region of the shapes boundary (I'm sorry I can't state a mathematical rule for this, but I'm sure there is one out there).