I am trying to better understand (standard, not gauge) 3d color codes. In particular, I am working with the lattice proposed in 1.
I understand how X error works, forming strings of the kind Vertex -> Cell -> Face -> Cell -> Vertex, where the Vertices and Faces are of the same color. (Notice that this is in the "dual picture", where qubits are at cells). An X error will happen if there is a string-net starting from one cell (qubit) and propagating to each face of the tetrahedra.
I would like to have a similar understanding of Z errors. From figure 2 in 2 it can be seen that Z logical errors propagate via the two-colored edges (we are in the dual picture, so faces -> edges) alternating edges of opposite coloring. For example red-yellow edge -> cell -> blue-green edge -> cell -> red-yellow edge.
What I am confused about is how Z logical errors look like. From 2 I would guess these have something to do with error branes encircling the face of the corresponding color, but I do not see it clearly.
My question is How do logical Z errors look like in this situation? Secondly, is it possible that I am getting it wrong that the lattice described in 1 and 3 can be used for non-gauge color codes?
Thanks a lot!
H. Bombin and M. A. Martin-Delgado, Topological Computation without Braiding
