You would speak of "vertexes". Tile a 3d space with cubes: you'll have faces, edges and vertexes. Curve the edges in smooth paths ("with continuous derivatives"): the vertexes disappear. But the equivalent of the 2d "corners" remain, as apparent in the 2d sections: no miracle happens.
The interesting part is the induction that by adding a dimension we may lose a "constraint".
You would speak of "vertexes". Tile a 3d space with cubes: you'll have faces, edges and vertexes. Curve the edges in smooth paths ("with continuous derivatives"): the vertexes disappear. But the equivalent of the 2d "corners" remain, as apparent in the 2d sections: no miracle happens.
The interesting part is the induction that by adding a dimension we may lose a "constraint".