## 4D Periodic Table

Ideas about how a world with more than three spatial dimensions would work - what laws of physics would be needed, how things would be built, how people would do things and so on.

### 4D Periodic Table

Assuming a universe in which atoms can form in 4d analogous to the way they do in 3d, there would be 1 s-orbital, 4 p-orbitals, 9 d-orbitals, and 16 f-orbitals. This would result in a periodic table with 198 elements. The equivalent of carbon is the atom with the atomic number of 7 (which I'll probably just call carbon), which forms 5 bonds in a pyrochoral arrangement. Nitrogen would have 2 equivalents, analogously to how there are both 2d surfaces (called "rotads" here due to being what rotation occurs over) and 3d planes in 4d. The first, which is probably the most analogous to nitrogen by the planar analogy, has 8 protons and 6 valence electrons - note that there is a decet rule in 4D rather than an octet rule. I can come up with several names for this element - carbonitrogen, tetragen, planogen, but I feel it's best to simply call this one nitrogen. The other nitrogen analog, oxynitrogen, triagen, or rotagen, forms 3 bonds, the same number as 3d nitrogen. Noticing now that any 4 points are coplanar in 4d space, meaning rotane molecules would be flat similar to water in 3d. Water still exists in 4d, as 4d oxygen with an atomic number of 10 forms 2 bonds. However, I don't know if water or rotane would be more chemically analogous to 3d water. They would both be polar, as would ammonia (planane / nitrane), which is (non-regular) pentachoral the same way 3d ammonia is (non-regular) tetrahedral.

The bonding angle in 4d is actually 104.47 degrees, compared to 3d's 109.47, meaning the ideal bonding angle is actually less than the angles of a pentagon. The 4d equivalent of graphene, planographene, is a truncated octahedral lattice. There is also rotographene, which is just regular graphene with more double bonds to account for the new decet rule, and forms a rotad in 4d (and thus, could be stacked like 3d logs). I believe that if structures resembling amino acids could be found in 4d, proteins would be possible, however I don't quite know how much of a chain you would need to form shapes... Perhaps tetronians would be rather tiny. (I do wonder what sugars would look like in 4d, perhaps they would be dodecahedral rather than pentagonal or hexagonal? What would platonic molecules look like in 4d? Could you have 4d buckyballs with 600 carbon atoms?)
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Dionian

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