# Mathematical word for geometrical object?

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 ?

• Are you talking about manifolds? Commented Jul 8, 2013 at 14:16
• Polytopes include all objects you mentioned except the circle, sphere and hypersphere. Commented Jul 8, 2013 at 14:40
• And is there a word less generic than manifold to designate polytopes+n-spheres ? Commented Jul 8, 2013 at 14:42
• They're rather different beasts to be honest. The polytopes are piecewise linear manifolds, where as the n-spheres are smooth differentiable manifolds. Commented Jul 8, 2013 at 14:52

## 1 Answer

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).