algorithmic modeling for Rhino
I have a geometry question that is challenging my idea of building an object made in rhino from planar surfaces:
I understand intuitively how regular convex polyhedra can have their faces be given thickness such that the sides of those new, thickened side solids are also planar-- i.e. a shell of a cube can be built from six solids that are extruded squares mitered at 45 degrees, or a square truncated pyramid. These pieces are easily fabricated.
My question is: under what conditions is this "planar miter" goal impossible? And, following that, is it possible to develop any planar-faceted solid into a thickened shell whose pieces all have planar sides as well as faces?
I've been using weaverbird's offset mesh to get started, see pictures for clarification...