  In this note the three dimensional Dirac operator $A_m$ with boundary
conditions, which are the analogue of the two dimensional zigzag boundary
conditions, is investigated. It is shown that $A_m$ is self-adjoint in
$L^2(\Omega;\mathbb{C}^4)$ for any open set $\Omega \subset \mathbb{R}^3$ and
its spectrum is described explicitly in terms of the spectrum of the Dirichlet
Laplacian in $\Omega$. In particular, whenever the spectrum of the Dirichlet
Laplacian is purely discrete, then also the spectrum of $A_m$ consists of
discrete eigenvalues that accumulate at $\pm \infty$ and one additional
eigenvalue of infinite multiplicity.
