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A heart shape as it is usually drawn (♥) consists of two smooth curve segments which join at two points, one at the top and one at the bottom. What is the most concise way to refer to these points?
I think cusps might be the right expression, but how do I call them in order to avoid ambiguity between the two? I thought about using convex and concave cusp, but then realized being convex or concave is relative to whether you look at the curve from the inside or from the outside.
This is indeed called a cusp. Two senses of that definition work well at the same time: the intersection of two curves, in general; and the reflection of a curve on itself.
You are right about the difficulty of convex or concave. For purely conversational English you might try internal and external, or for the heart shape per se, upper and lower would probably be generally understood.
