  The amplituhedra arise as images of the totally nonnegative Grassmannians by
projections that are induced by linear maps. They were introduced in Physics by
Arkani-Hamed \& Trnka (Journal of High Energy Physics, 2014) as model spaces
that should provide a better understanding of the scattering amplitudes of
quantum field theories. The topology of the amplituhedra has been known only in
a few special cases, where they turned out to be homeomorphic to balls. The
amplituhedra are special cases of Grassmann polytopes introduced by Lam
(Current Developments in Mathematics 2014, Int.\ Press). In this paper we show
that that some further amplituhedra are homeomorphic to balls, and that some
more Grassmann polytopes and amplituhedra are contractible.
