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A smooth cube manifold M n is a smooth n-manifold M together with a smooth cubulation on M . (A smooth cubulation is similar to a smooth triangulation, but with cubes instead of simplices). The cube structure provides, for each open k-subcubeσ k , rays that are normal toσ. Using these rays we can construct normal charts of the form D n−k ×σ → M , where we are identifying D n−k with the cone over the link ofσ (these identifications are arbitrary and the identification between ∂D n−k and the linkdoi:10.4310/ajm.2016.v20.n4.a6 fatcat:34cuyakc4jbijomtvv7xaarcpu