Frustration in classical spin models can lead to degenerate ground states without long-range order. In reciprocal space, these degeneracies appear as manifolds of wave vectors, their dimensionality increasing with the degree of frustration and the robustness of the disordered spin-liquid state. Here, we present a recipe to explicitly construct Heisenberg models on Bravais lattices with codimension-one manifolds, i.e., lines in two dimensions and surfaces with different Euler characteristics in three dimensions. Furthermore, we discuss the role of thermal and quantum fluctuations in stabilizing ordered states.