I have more or less dropped my attempts at making a single-prim analog clock, until I have abruptly bumped into a solution, used expressly for this purpose in the Japanese lands. All credit for this trick goes to kit Pizzicato, who sells them under the label *chronokit* — whether the original inventor of the trick is the maker of the clock, I don’t know, but, I’ve figured out how they did it and am going to tell anyone who cares, now. 🙂
The mystery shape is a Ring type prim, with around 75.0 hollow, Triangle hollow shape, and a 0.25-0.75 profile cut. Chopping a ring up like that results in a round object with at least three individually texturable faces visible from one direction, depending on other parameters — the limit you can twist it into would be five. By default, the texture on these faces is distorted in a non-linear fashion. However, if you switch the texture mapping to planar, on at least three of the faces the distortion will become linear, and you can use a rotated flat texture to create a clock face and a minutes and seconds hand with no unusual scripting required.