Spacefiller

$ \def\T{\mathcal T} % tiling \def\P{\mathcal P} % protoset $

In the theory of tilings a spacefiller is a prototile that admits a monohedral tiling.

In other words, a tile $T$ is a spacefiller iff there is a tiling $ \T = \{ T_i \} $ such that all its tiles $T_i$ are congruent to $T$.

Simple examples of spacefillers are all triangles and all quadrangles for the plane, and all parallelepipeds for the space.