I have wondered why the "walls and voids" of the cosmological galaxy distribution seem to resemble a "foam", like rising bread that's ready to fall, with "voids" corresponding to empty bubbles in the foam. James K and Rob Jeffers https://astronomy.stackexchange.com/a/18610/14485 seem to be saying local matter tends to relatively "overrule" the cosmological expansion, and that the bubbles ("voids") get relatively more cosmic expansion. This may explain the "foam" appearance: local large areas of slightly lower relative galaxy density will tend to cosmic expansion more, and will grow (less dense) more than denser regions, like bubbles in the foam, effectively driving all the galaxies into the walls between the bubbles.
Sorry I have not enough reputation to comment. I am not going to give a full answer as I am on my phone.
I guess there is a (at least seemingly) neat mathematical explanation for the geometry. But it is simply a result of gravitational collapse. The degree of 'formy-ness' depends on cosmology (for example, need more / less time to form structures depending on cosmology). If you have random distribution of matter in infinite 3d with slight density fluctuation, some patch of the space become denser faster than other patches and become even denser and so on. Every matter pulling each other while clustering themselves results in 3d to 2d, 2d to 1d, 1d to 0d structure of overdensity. So most dense regions are point-like structures (super clusters), and next most dense regions are filamentary, then sheets. The rest are voids. Cosmic expansion changes the strength of gravitational pulling but does not really alter the 'shape' or direction of force, hence little effect on the 'formy-ness' of voids. As long as it is a cosmology with collisionless darkmatter, the same formy structure will form given enough time. Cosmological N body simulations use fixed(comoving) volume where only the magnitude of gravitation changes due to the cosmic expansion. And in those simulations you can see (and that's where astronomers learned about) the cosmic structures. There are many movies of cosmological simulations you can easily find.