The post clearly described a non-convex shape, and "flat-surfaced shape" should be a pretty clear instruction as well. The shape described may be visualized as a cylinder with a cone cut out, where the base of the cone aligns with one of the bases of the cylinder, and its tip with the center point of the other cylinder base. Except that the cylinder may be modified so that, seen in a cross-section, the line going from the base to the tip on either side may be a (convex or concave) curve. It makes sense as a starting point in the search for a shape with the desired properties. And it can immediately be seen to be non-convex in both described configurations, given that there's a cavity cut out.