This dataset contains four files describing the rays of secondary fan of the hypersimplex(2,7). hypersimplex_2_7_idmap.dat.xz maps IDs to the rays of the secondary fan, such that we may refer to the rays by that ID. hypersimplex_2_7_orbit_representatives.dat.xz maps orbit sizes to sets of IDs of rays with that orbit size, but only one ray per orbit hypersimplex_2_7_histogram.dat.xz maps spreads to sets of IDs of rays with that spread hypersimplex_2_7_orbit_histogram.dat.xz maps orbit sizes to sets of IDs of rays with that orbit size. The datasets are compressed using xz and can be read using polymake. The datasets were computed from the regular triangulations of the hypersimplex(2,7). Since these triangulations only came up to group action, first the secondary cone was computed for such a triangulation, then the rays were computed and subsequently the orbits of the rays were expanded.