The family of vector spaces (\mathcal{T}_{n,\pm})_{n \in \mathbb{N}} generated by the planar tangles having 2n intervals on their output disk and a white (or black) \star -marked interval, admits a planar algebra structure.
The Temperley-Lieb-Jones planar algebra \mathcal{TLJ}(\delta) is generated by the planar tangles without input disk; its 3-box space \mathcal{TLJ}_{3,+}(\delta) is generated by .