The tetrahedral scheme in (3+1)D  is somewhat similar to the hexagonal scheme in (2+1)D, in that the grid is divided evenly into two sets of points, at which updating is performed using ``mirror-image'' stencils. It is different, however, because grid points can easily be indexed with reference to a regular cubic lattice; the hexagonal scheme operates on a rectangular grid in stretched or transformed coordinates. In fact, a tetrahedral scheme can be obtained directly from an octahedral scheme simply by removing half of the grid points it employs; as such, any given grid point in the tetrahedral scheme has four nearest neighbors. As usual, we assume the nearest-neighbor grid spacing to be . See Figure 12(a) for a representation of the numerical grid.
As per the hexagonal scheme, we will view this as a vectorized scheme operating on two distinct sub grids, labelled 1 and 2 in Figure 12(a). The two grid functions
are defined for integers , and all even such that is also even.
will be used to approximate a continuous function at the point with coordinates
approximates at coordinates
. The numerical scheme can then be written as
As for the hexagonal scheme, we may check consistency of this system with the wave equation by treating the grid functions as samples of continuous functions and and expanding (32) in terms of partial derivatives; both grid functions updated according to this scheme will approximate the solution to the wave equation on their respective grids.
Determining the stability condition proceeds as in the hexagonal scheme; taking spatial Fourier transforms of (32) gives a vector spectral update equation of the form (10), with given by
The computational and add densities of this scheme, in general, are