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Reality isn’t a grid of pixels of any shape. If it were, I suspect the Michelson-Morley experiment would’ve gone differently.
But if it were, the pixels would be some at-least-4-dimensional shape.
Fun fact: many early video games didn’t have pixels (even in the CRT sense of the word)
Answer this definitively, and win yourself a Nobel prize!
Many of the leading physicists in today's age think the shape is a little 'string,' if you will.
Why is #1 an issue? You're assuming physics at a subatomic level works the same as that at a macroscopic level, but they don't. Things don't have well defined boundaries.
I think the premise of a „pixel“ being the smallest entity in software is not right. Rasterization, i.e. translating (actually reducing) a defined subset of the software state into a 2D grid of colored pixels, is only a very limited view on that software.
This might be the reason for the different answers we‘re getting here. Most aim for subatomic physics, it we could also go to light theory (photons and wave frequencies/resolution) and human retinas, general optics and electron microscopes, which again would end up at subatomic physics (you got my circle-train of thought here).
I don't think it's likely that there is a minimum volume, at least not a discrete quantized one. It would have to be a [regular honeycomb tessellation](https://en.wikipedia.org/wiki/Honeycomb_(geometry)) that shows no bias towards any particular direction (i.e. no corners). There are no shapes that fulfill both of those conditions in 3D space.
In 3D space it's called a voxel
Hexagons are the bestagons.
See the other answers for why this isn't really right, but given 4 dimensional spacetime, if that 'pixel' did exist, it would look like a hypercube/tessaract. A constantly stretching and twisting but approximate one, anyway.