i will show how to construct a very large family of new examples of convex ancient and translating solutions to mean curvature flow in all dimensions. at $t=-\infty$, these examples resemble a family of standard grim hyperplanes of certain prescribed orientations. the existence of such examples has been suggested by hamilton and huisken—sinestrari. our examples include solutions with symmetry group $d\times \mathbb z_2$, where $d$ is the symmetry group of any given regular polytope, and, surprisingly, many examples which admit only a single reflection symmetry. we also exhibit a family of eternal solutions which do not evolve by translation, settling a conjecture of brian white in the negative. time permitting, i will present further structure and partial classification results for this class of solutions, as well as some open questions and conjectures. \\ \\ joint with t. bourni and g. tinaglia.