A net is prime if every triangular circuit bounds a face. Non-prime neoplatonics decompose along their separating triangles into prime pieces; the three construction types below follow the paper. Captions give the decomposition.
All face-to-face gluings of tetrahedra through eleven tets (v ≤ 14), enumerated under the degree bound: one class at two and at three tets, three at four and at five; from six through eleven, only the helical path.
Two or more octahedra glued face to face.
One to four tetrahedra on the faces of a prime core other than the tetrahedron. The octahedron core is complete: all eight attachment classes up to symmetry.