ABSTRACT
Centered twist tiles come in different varieties because we can vary the size of the central twist polygon. With centered twist triangle tiles, the twist angle for a triangle was independent of the corner angles of the triangle, just as it was independent of the number of sides for regular polygons. In centered twist tilings, all of the twist angles are the same. That means that the fewer-sided polygons are closer to their critical values, while larger polygons have holes in their twists. For each polygon twist, there are various distinct ways of flattening it, but they result in very different appearances, both in the crease pattern and the folded form. For some polygons—notably parallelograms—both centered twist and offset twist constructions give rise to retrograde central polygons. Offset twist tiles are a different genus from centered twist tiles.
