1. A color gamut surface generating apparatus comprising a vertex generating unit, wherein a device-dependent color space has axes of (i) four basic colors including black and (ii) at least one extra color which are used in color output by an output device, and the vertex generating unit generates, in the device-dependent color space, vertices of each of sub-surfaces constituting a surface of a color gamut by selecting (a) at least one color gamut each of which is output by the output device using a combination of three of the basic colors and one, corresponding to each color gamut, of the at least one extra color, and (b) a color gamut which is output by the output device using the four basic colors; and a gamut surface generating unit that generates surface points existing on the surface of the color gamut constituted by the vertices.