Possibilities of increasing the critical error rate of quantum key distribution (QKD) protocols are investigated. We consider QKD protocols with discrete alphabets, letters of which form regular polyhedrons on the Bloch sphere (tetrahedron, octahedron, cube, icosahedron, and dodecahedron, which have 4, 6, 8, 12, and 20 vertices respectively) and a QKD protocol with continuous alphabet, which corresponds to the limiting case of a polyhedron with infinite number of vertices. The stability of such QKD protocols against intercept–resend and optimal eavesdropping attacks on the individual information carriers is studied in detail. It is shown that all these QKD protocols have approximately the same critical error rates. In the case of optimal eavesdropping strategies, after basis reconciliation, the QKD protocol with continuous alphabet surpasses all other protocols in terms of noise-resistance. Without basis reconciliation the protocol with the highest critical error rate has a tetrahedron-type alphabet. Additional increase of the dimensionality of the quantum alphabet leads to a further increase of the critical error rate.