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In the framework of a relativistic extension of the three‐constituent–quark model of the proton, spinors of third rank in Dirac indices are used to express covariantly the spin structure of S‐state baryons of spin 1/2 or 3/2. These spinors are defined directly in terms of 4‐spinors of the Dirac space D, and classified according to the irreducible representations of both the (internal) Lorentz spin group acting on E=D×D×D, and the permutation group S3. All possible combinations of spin, flavor, and momentum distributions of quarks in S‐state baryons are considered from the point of view of S3. We also suggest the possibility of defining Dirac matrices acting on E, which may prove important in view of studying three‐quark confinement forces through an effective relativistic wave equation for the proton.