Color gamut boundaries in CIELAB space are determined for two CIE standard observers, CIE 1931 2° and CIE 1964 10°, under two illuminants, D₅₀ and D₆₅, using spectral and optimal stimuli. Computational methods and formulas based on Grassmann's law are given. Two-dimensional projection of the computed color gamut provides the boundary for all possible stimuli, real and imaginary, and is the closest analogue to the chromaticity diagram of the CIEXYZ or CIELUV space. We also discuss reasons of no chromaticity diagram in CIELAB space. This computation leads to the derivation of the most saturated primary colors for block dyes. Two-dimensional gamut projections of several sets of block dyes are then computed under conditions of the CIE 1931 color match functions and illuminants D₅₀ and D₆₅. The validity of the Grassmann's law is examined for additive and subtractive color mixing of block dyes. Finally, color gamut boundaries of two real devices are presented for comparisons.