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Let $A$ be a central simple algebra over a number field $K$ with ring ofintegers $\mathcal{O}_K$, such that either the degree of the algebra $n \ge 3$,or $n=2$ and $A$ is not a totally definite quaternion algebra. Then strongapproximation holds in $A$, which allows us to describe the genus of an$\mathcal{O}_K$-order $\Gamma \subset A$ in terms of idelic quotients of thefield $K$. We consider orders $\Gamma$ that are tiled at every finite place$\nu$ of $K$ and use the Bruhat-Tits building for $SL_n(K_\nu)$ to give ageometric description for the local normalizers of $\Gamma$. We also giveexplicit formulas and algorithms to compute the type number of $\Gamma$. Ourresults generalize work of Vign\'{e}ras for orders in higher degree centralsimple algebras.

Type numbers of locally tiled orders in central simple algebras