“How many angels can fit on the head of a pin?” is a question that comes to mind, all too often, when trying to connect too many timbers together at any one spot. This comes up, most regularly, in polygonal structures such as the King Arthur Flour dodecagonal (twelve-sided, for the Latin-impaired) building in Norwich, VT. At the top of this forty five foot tall, sixteen foot wide tower is a coopered king post to die for. The dozen rafters had no trouble finding a place to land at the top of the king (or crown) post, but the twelve horizontal timbers at the loft level were beyond jostling for space. What to do? The first part of the strategy is to cut the problem in half, by cutting off six of the radial members and putting wedged through tenons on them after they passed through a circumferential ring of headers. I connected the three opposing pairs of timbers that still made it to the axis with three separate radial splines that pass through the coopered post. In order to avoid THESE from colliding, I spread them vertically along the axis of the tower. The three splines spiral by one another, within the confines of the king post. The three pairs of timbers had to be unusually deep, to accept the vertical distribution within six coplanar timbers: a high, low, and mid-spline.