Lobke, and other constructions from conical segments

Lobke is a mathematical sculpture designed and constructed by Koos Verhoeff, using conical segments. We analyze its construction and describe a generalization, similar in overall structure but with a varying number of lobes. Next, we investigate a further generalization, where conical segments are connected in different ways to construct a closed strip. We extend 3D turtle geometry with a command to generate strips of connected conical segments, and present a number of interesting shapes based on congruent conical segments. Finally, we show how this relates to the skew miter joints and regular constant-torsion 3D polygons that we studied earlier.