  A large number of examples of compact $G_2$ manifolds, relevant to
supersymmetric compactifications of M-Theory to four dimensions, can be
constructed by forming a twisted connected sum of two appropriate building
blocks times a circle. These building blocks, which are appropriate $K3$-fibred
threefolds, are shown to have a natural and elegant construction in terms of
tops, which parallels the construction of Calabi-Yau manifolds via reflexive
polytopes.
