Part of Greg Egan novel Diaspora takes place in a universe with 5 spatial dimensions.
Why? Well, apparently ants have 6 legs because this allows tripod-gait, a simple leg movement that always keeps 3 stable points on the ground[1]
In 4D, you'd need 4 points on the ground, hence tetra-pod gait (4+4 legs).
You could of course do with less, I'd guess even as low as 1-2 if you have lots of muscles and good balance.
Awesome book regardless.