network to obtain robustness to different spiral samples, it inevitably has to become invariant to different rotations of the neighbourhoods, thus it has reduced capacity. To this end, we emphasise the need of consistent orderings across different meshes. Moreover, in [@spirals], the authors model the vertices on the spiral via a recurrent network, which has higher computational complexity, is harder to optimise and does not take advantage of the stationary properties of the 3D shape (local statistics are repeated across different patches), which are treated by our spiral kernel with weight sharing.

**Comparison to spectral filters:** Spectral convolutional operators developed in [@chebnet; @kipfGCN] for graphs and used in [@coma] for mesh autoencoders, suffer from the fact that the are inherently [*isotropic*]{}. This is a side-effect when one, under the absence of a canonical ordering, needs to design a permutation-invariant operator with small number of parameters. In particular, spectral filters rely on the [*Laplacian operator*]{}, which performs a weighted averaging of the neighbour vertices : $$(\Delta f)_x = \sum\nolimits_{y: (x,y) \in \mathcal{E}} w_{xy} \big(f(y) - f(x)\big),$$ where $w_{xy}$ denotes an edge weight. A polynomial of degree $r$ with learnable coefficients $\theta_0, \hdots, \theta_r$ is then applied to $\Delta$. Then, the graph 