1. A color gamut boundary information generating device comprising: a receiving unit that receives a plurality of pieces of coordinate information indicating a plurality of points in a color space that is independent of an output device, respectively; a tetrahedralizing unit that performs a tetrahedralization process, with the plurality of points in the color space specified by the plurality of pieces of coordinate information received by the receiving unit serving as vertexes; a first generating unit that generates boundary information, which is a set of outermost triangular faces forming a convex hull among triangular faces obtained through the tetrahedralization process; and a correcting unit that selects one of the triangular faces included in the boundary information generated by the first generating unit, the selected triangular face serving as a target face, regards a tetrahedron including the target face as a target tetrahedron, determines whether or not the target tetrahedron satisfies a predetermined condition, and, if the target tetrahedron does not satisfy the predetermined condition, selects the triangular faces included in the target tetrahedron except the target face, eliminates the target face from the boundary information, and adds the selected triangular faces to the boundary information, thereby correcting the boundary information.