The X neighborhood is a sister partitioning scheme to the one used in the Margolus neighbourhood. It exhibits very similar behaviour when used with appropriately translated automata. It has cells with 16 states, and uses information from neighbours in an 'X' configuration.
It is an isometric neightbourhood.
When implemented in hardware, it applies the same transformation to each cell on each clock tick - and requires no apparatus to implement an alternating partitioning grid.
It also has some corresponding drawbacks, however:
More diagrams of this neighbourhood are available here.
There are partitioning schemes from the same family available with triangular geometry.
The automata may be generalised into three dimensions. Pictures of such automata are available here.