There are many (planar) lattices: standard square grid lattice, hexagonal lattice, triangular lattice, Lieb lattice, Kagome lattice...

Consider the standard square lattice on $\mathbb Z^2$ (each vertex has valency four) and add `non-crossing' diagonals to each face of this graph (we do not add any new vertices). Now each vertex has valency eight.

(An equivalent way to define this graph is to say that each point of $\mathbb Z^2$ is connected with the 8 nearest neighbors.)

Is there a name for such a graph? I have seem something like `a strong product of two infinite paths', but I cannot make any sense of it.

There are many (planar) lattices: standard square grid lattice, hexagonal lattice, triangular lattice, Lieb lattice, Kagome lattice, dice lattice...

Consider the standard square lattice on $\mathbb Z^2$ (each vertex has valency four) and add `non-crossing' diagonals to each face of this graph (we do not add any new vertices). Now each vertex has valency eight.

(An equivalent way to define this graph is to say that each point of $\mathbb Z^2$ is connected with the 8 nearest neighbors.)

Is there a name for such a graph? I have seem something like `a strong product of two infinite paths', but I cannot make any sense of it.

There are many (planar) lattices: standard square grid lattice, hexagonal lattice, triangular lattice, Lieb lattice, Kagome lattice...

Consider the standard square lattice on $\mathbb Z^2$ (each vertex has valency four) and add non-crossing diagonals to each face of this graph (we do not add any new vertices). Now each vertex has valency eight.

Is there a name for such a graph? I have seem something like `a strong product of two infinite paths', but I cannot make any sense of it.

There are many (planar) lattices: standard square grid lattice, hexagonal lattice, triangular lattice, Lieb lattice, Kagome lattice...

Consider the standard square lattice on $\mathbb Z^2$ (each vertex has valency four) and add `non-crossing' diagonals to each face of this graph (we do not add any new vertices). Now each vertex has valency eight.

(An equivalent way to define this graph is to say that each point of $\mathbb Z^2$ is connected with the 8 nearest neighbors.)

Is there a name for such a graph? I have seem something like `a strong product of two infinite paths', but I cannot make any sense of it.