That is what capsule networks were designed to solve. So far though I've only heard they got good results on MNIST and promising results on CIFAR10.

Anyway I'm not sure that you can conclude that just because convolutions are 2D that deep neural networks are unable to understand 3D relations. For example this network seems to have a pretty good understanding of the 3D world:

https://deepmind.com/blog/neural-scene-representation-and-re...