Software credit: see http://www.software3d.com/Stella.php to try or buy the software I used to make this. It’s called *Stella 4d*.

# Monthly Archives: April 2014

## On the Varieties of Water

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As many people know, there is more than one type of water. For example, the term “heavy water” often refers specifically to D_{2}O, with “semi-heavy water” referring to DOH. Add tritium to the mix, and the new combinations possible — all radioactive — include HOT, DOT, and T_{2}O. Along with diprotium oxide, plain old H_{2}O, that’s six isotopic variants of this one simple compound.

However, that six needs to be multiplied by three. Why? Because there’s one set of six that includes an oxygen-16 atom (the usual kind), and another six for oxygen-17, and one more for oxygen-18, for a total of eighteen. So far. Both oxygen-17 and -18 are stable, and occur in nature, although they are both of very low abundance.

Eighteen kinds of water, half of them radioactive? No, that’s not quite enough. If the radioactive isotope of hydrogen is included, then so should be the radioisotopes of oxygen. That would include oxygen isotopes with mass numbers from 13 to 15 (add three more sets of six, or 18, which, when added to the original 18, gives a running total of 36), and 19 to 24 (add six more sets of six, or 36 more, to the 36 we just had, and we’re now at 72).

To leave it at 72 isotopic varieties of water is not necessary, but it is reasonable. Yes, there is oxygen-26, but with an estimated half-life of 40 nanoseconds, it isn’t reasonable to expect there to be time for it to form a water molecule. Could it happen? Possibly — but it’s extremely unlikely to ever be observed. For oxygen-12, the story is similar, but with an even shorter nuclide-lifetime than that of O-26.

Additional isotopes of hydrogen have also been detected, with mass numbers from 4 to 7, but they decay even more quickly than O-26 as well.

72 it is, then, counting nothing with a half-life under a millisecond. This is the sort of thing that happens when math compulsives think about chemistry a bit too long.

## Three-Color Tessellation Using Biconcave Octagons

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## Three-Color Tessellation: A Modification of the Tiling of the Plane with Regular Hexagons

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In each case, modifications along hexagon-edges were made using equilateral triangles. Every segment in this tessellation has equal length, also, which required trisection of the original hexagons’ sides.

## Pentagonal Mandala III

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I suspect that this could be continued outward indefinitely, as a radial and aperiodic tessellation, using only the four polygons you see, repeatedly, here. However, I have no proof of this.

## Pentagonal Mandala II

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## Octagons Can Tile a Plane

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This tessellation is made entirely of octagons. Half of them are regular, while the other half are equilateral and tetraconcave.