I'm fond of the idea of "impossible" geometric planets. In fact, I'd like an assortment! Disc worlds, tetrahedrons, regular dodecs, cubes, octahedrons... I think it would be fun to have sectors have a randomized array of different shapes as well as biome types. Also, I'm okay with the weird angles. Figuring out how to navigate a tetra world's edges would just be a hazard of exploration.
I recall reading a wierd webcomic some years ago about a fractal universe with triangular 'world plates' that were gravitationally held in place in a Sierpinski triangle arrangement, and if you weren't careful, you could fall off the world...
Edit: Actually, wouldn't worlds with fewer faces reduce some of the lag?