Pankov and Tyc have shown that a unicursal (a.k.a., z-knotted) deltahedron may have up to four types of triangle faces, and that these four types determine its compatibility in forming connected sums with other unicursal deltahedra when the sum is constrained to be unicursal. In such case, all three deltahedra, the sum and the two summands, can be wrap-formed. Presented with a wrap-formed deltahedron, how can we most easily assign types to its triangles?
Given a triangle, read the roadcodes of its 3 edges. if any starts with a even number: the triangle is SOLO if any two start with an odd number: the triangle is UNISON get the triangle's STRADDLE ORIENTATION from any edge that starts with an odd number: when you are comfortably reading both numbers, edge's orientation is upward. get the triangle's LAYER ORIENTATION from the 3 numbers visible on the triangle's face: by visiting them in increasing order if both orientations agree: the triangle is CONCORD else: the triangle is DISCORD Type from this mapping: o = UNISON and CONCORD (M1) * = UNISON and DISCORD (M2) + = SOLO and DISCORD (M3) - = SOLO and CONCORD (M4)
