We derive analytical expressions for the central and side quantizers in an n-channel symmetric multiple-description lattice vector quantizer which, under high-resolution assumptions, minimize the expected distortion subject to entropy constraints on the side descriptions for given packet-loss probabilities. The performance of the central quantizer is lattice dependent whereas the performance of the side quantizers is lattice independent. In fact the normalized second moments of the side quantizers are given by that of an L-dimensional sphere. Furthermore, our analytical results reveal a simple way to determine the optimum number of descriptions. We verify theoretical results with numerical experiments and show that with a packet-loss probability of 5%, a gain of 9.1 dB in MSE over state-of-the-art two-description systems can be achieved when quantizing a two-dimensional unit-variance Gaussian source using a total bit budget of 15 bits/dimension and using three descriptions. With 20% packet loss, a similar experiment reveals an MSE reduction of 10.6 dB when using four descriptions.