EVEN ATOMS HAVE TETRAHEDRAL SHAPES,
BECAUSE OF A BIZARRE PROPERTY OF ELECTRONS
In addition to -- or perhaps because of -- the fact that tetrahedrons are the strongest and most stable 3-dimensional shapes that can possibly exist in the universe as we know it, atoms and molecules also have tetrahedral shapes.
Around ANY type of atom larger than hydrogen and helium, the arrangement of electrons is so curious, and so apparently illogical, that it would be called bizarre, and nonsensical, if it were not well-known, and totally real.
As a simplified basic introduction, here is a basic starting point, for anyone who wants to go digging farther into this topic, and reach a level where they can at least: (i) know how to look for more information, or (ii) have an intelligent discussion, with a chemist, about these matters.
For any and all elements heavier than hydrogen or helium:
1. The FIRST FOUR electrons in the series of elements that occupy the first full "row" of a periodic table, stay as far away from each other as they possibly can, until exactly FOUR of them have arrived. Why? Because they all have negative charges; and, therefore, they all repel each other, and want to stay as far away as possible, from each other. This places them in tetrahedral shape (or, more precisely, a four-part "probability cloud" which has a tetrahedral shape), around the nucleus of the atom, in a way that can be illustrated as follows:
When drawn on paper or depicted in a book, the most common way to depict those shapes is by a "flattened" 2-dimensional drawing, as shown below, which depicts the nucleus in black, and electrons in red. As mentioned above, the electrons stay as far apart as they can from each other, since they all have the same (negative) charge.
So far, so good; that's the easy part. What happens next seeems to defy logic and reason. When the NEXT four electrons arrive, they somehow begin a process, where each NEW electron "pairs up" with an electron which was already there. Here are the conventional "flattened" depictions, for elements which have 5, 6, 7, or 8 electrons, in their outermost "valence" shell (and, the outermost "valence" electrons are the ONLY electrons, in any atom, which can and will react with other atoms).
If you ask a chemist, "Why do they do THAT? How is that even possible? Don't ALL electrons repel each other, since ALL of them have negative charges?", the closest s/he can give you, to an answer, will be along the lines of, "Well, we don't really know, so we made up the phrases "left spin" and "right spin", to describe how two electrons can pair up with each other. Are the electrons actually `spinning'? No, not really; but, that term lets us apply the modifiers `left' and 'right', and those terms can help people at least begin to understand what is happening, because people are familiar with how a left hand, and a right hand, can interact with each other, in comfortable, functional ways."
The NEXT bizarre and illogical thing to try to understand, is this: once a "valence shell" of electrons gets full, it effectively becomes "locked in", and sealed in, and "set into concrete" in an amazingly strong, solid, stable, and durable way. And, in this context, the term "durable" pretty well means, "for the entire remaining life of the planet, moon, asteroid, rock, or gas molecule that that molecule is part of". The only exceptions involve atoms that are undergoing true "nuclear" reactions (which occur mainly inside stars; the only normal and natural exception, anywhere in or on Planet Earth, occurs when uranium atoms decay, and break apart into smaller atoms).
And, the electrons in ANY already-full, already-completed "orbital electron shell" of electrons which surround any atom (i.e., INSIDE a valence shell, which always and necessarily is larger than any of the smaller internal "orbital" shells) will NEVER, EVER react with any OTHER electrons (except, again, in true "nuclear" reactions, which excludes any chemical reaction that will ever occur naturally on or in Planet Earth, with the sole exception of uranium atoms, decaying).
The absolute innermost "orbital shell" of electrons, around ANY atom, has only one electron (for hydrogen), or two electrons (for helium). Somehow, for some reason, that super-small innermost shell has only two electrons, and the "probability cloud" which describes where those two electrons are, is a simple sphere.
After THAT, that the shapes of each and both of the NEXT TWO valence shells, becomes tetrahedral. Those elements are shown in this "mashed-up" version of rows 2 and 3, from any periodic table:
Logical arrangement -
electrons 1-4 stay as far apart from each other as possible
Illogical arrangement -
electrons 5-8 pair up with electrons 1-4, in tetrahedral shapes
The fact that atoms, themselves, have tetrahedral shapes, in bizarre and illogical ways that arise from pairings of electrons that normally should repel each other, raises questions that go beyond science, into philosophy, and even religion. If anyone wants to truly understand tetrahedrons, they need to at least try to realize that that shape -- the strongest and most stable 3-dimensional shape that can possibly exist, in the universe as we know it -- somehow even extends all the way down, even to individual atoms.