The paper calculates limits to the performance of low-rate block-oriented coding and coded modulation schemes, such as spherical coding. The method is appropriate to fairly lowrate communication systems, in terms of bit rate per unit bandwidth. An approach based onn-dimensional geometry is used to derive an ideal geometric structure for such codes based on the form of a regular polytope with simplex cells. This structure is in general unrealisable, but its performance would give a limit to the performance of any practical code. Its performance in terms of the coding gain achievable is therefore calculated in order to find that limit. Maximum coding gain is found to be dependent on code length (equivalent to number of dimensions) and to a lesser extent on code rate. For a code length of 24 and rate 0.5 a coding gain of nearly 5 dB is possible, and in general the coding gain increases by 1 to 1.5 dB for every doubling of the number of dimensions.