Before I go back to the adventures with tetrahedrane, I thought I would take a short break to talk about group theory. I started learning group theory seriously some time back, as a part of chemistry course. Till now I had seen notations like \(D_{h}\)and \(T_{d}\) and had secretly wondered what they were with a vague feeling that they somehow represented what the molecule looked like. My footing in rigorous math is at best questionable, so pardon me wherever I might not be that precise. Groups are an abstract collections of things/objects (as it might be evident from the name) with a particular operations defines between elements (like addition or multiplication) that obey particular properties. The most obvious and oldest of groups are things known as rotation groups. They are what they sound like: groups which are collection of all the rotations you can do. For example Euler's theorem says that any rotations of an object be it a chair or a planet where a point in the body r...
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