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 ?

  • $\begingroup$ Are you talking about manifolds? $\endgroup$
    – Sigur
    Commented Jul 8, 2013 at 14:16
  • 1
    $\begingroup$ Polytopes include all objects you mentioned except the circle, sphere and hypersphere. $\endgroup$
    – user5402
    Commented Jul 8, 2013 at 14:40
  • $\begingroup$ And is there a word less generic than manifold to designate polytopes+n-spheres ? $\endgroup$
    – Vincent
    Commented Jul 8, 2013 at 14:42
  • 1
    $\begingroup$ They're rather different beasts to be honest. The polytopes are piecewise linear manifolds, where as the n-spheres are smooth differentiable manifolds. $\endgroup$
    – Dan Rust
    Commented Jul 8, 2013 at 14:52

1 Answer 1


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).


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