Is there a mathematical word to designate the concept of a geometrical object like:
- square
- cube
- tesseract
- N-dimensional cube
- circle
- sphere
- hypersphere
- regular and non-regular polygons
- regular and non-regular polyhedrons
- ...
What is the common word to designate all these objects ?
They are all compact subsets of suitable $\mathbb R^n$. I would call them manifolds in a broad sense, considering both the cases "manifold with corners"-"manifold without corners" (but with boundary).