I've got a bunch of simple geometric shapes that don't seem to be easily constructed with the basic geoms, and I'm trying to model them. Some simple ones: Pyramid Cone Triangular Prism Hexagonal Prism Half-sphere If I had these shapes it would be much easier to make more complex shapes, but it seems hard to make these shapes purely out of existing geoms. The alternative seems to be meshes, but my intuition is that there are simple closed-form contact equations for each of them similar to existing shapes. Are meshes much more inefficient than simple geoms? Not exactly these but similar: http://www.hand2mind.com/item/mini-geosolids/7695

You need meshes to represent anything that is not a primitive MuJoCo geom. The collision detection mechanism is indeed faster when you have analytical surfaces that support certain computations, but with pyramids and prisms this is not the case, so meshes are just as efficient. Cone and half-sphere collisions would have been faster if MuJoCo supported them natively. In general though, collision detection is rarely the bottleneck in terms of computation.