Abstract: We present an algorithm for the reconstruction of a surface with boundaries (including a non-orientable one) in three dimensions from a sufficiently dense sample. It is guaranteed that the output is isotopic to the unknown sampled surface. No previously known algorithm guarantees isotopic or homeomorphic reconstruction of surfaces with boundaries. Our algorithm is surprisingly simple. It ‘peels’ slivers greedily from an α-complex of a sample of the surface. No other post-processing is necessary. We provide several experimental results from an implementation of our basic algorithm and also a modified version of it.