This record contains all reflexive simplices of dimension two to six. We use the HDF5 format to store the simplices. The data are organized by dimension, with datasets named dim2, dim3, dim4, dim5, and dim6. Each dataset is three-dimensional with size $(d, d+1, N)$, where $d$ is the simplex dimension and $N$ the number of simplices. Each slice $M[:, :, i]$ contains integer lattice coordinates of the vertices of one reflexive simplex. The data were generated using the algorithm described in the accompanying article.