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Violet-dyed dodecahedral lumps of transparent sugar crystals for use in coffee, carved or moulded, which will dissolve more quickly because their shape is more nearly spherical. Better than sugar balls because they don't roll, more stable than icosahedra because they only have twelve faces.
Tetrahedral_20bricks
[hippo, Oct 24 2008]
Sugar dodecahedra - Baked
http://www.candyfab....php/heater2results
But not violet. [Loris, Oct 26 2008]
Menger Dodecahedron
http://www.shapeway...r_dodecahedron.html
(sort of) [nineteenthly, Oct 26 2008]
Menger sponge
http://en.wikipedia.../wiki/Menger_sponge
Recursize space-filling structure [HughBothwell, Oct 26 2008]
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Annotation:
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//which will dissolve more quickly because their shape is more nearly spherical// - you mean "more slowly" - they'll have less surface area per unit volume than cubes. |
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Oh bugger.
OK, make that "slow release sugar dodecahedra for hypoglycaemia or diabetics or something". |
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yeah, yeah, that sounds much better - great idea |
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Horses like sugar cubes, therefore this could be used to teach them basic lessons in geometry with a bit of re-writing. (+) |
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anything that can be used to teach geometry to horses gets a bun from me ! |
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How about a whole Sugar Platonic Solids set in a tasteful gift box? |
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...and when you open the lid, Stephen Hawking's voice synthesiser reads out Euclid's proof that there are only 5 Platonic solids, over a background of soothing wind chimes. |
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Yes! I was just thinking that tetrahedral sugar would dissolve fastest. Thanks, [Jutta], clearly the way to go.
And to go too far, how about pentose dodecahedra, tetrose sugar cubes and the three others of triose? |
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I'm certainly up for the Platonic Sugar Solids gift set. |
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And if they made tetrahedral sugar lumps, I would definitely buy them. They'd even pack neatly too, and have much more diverse possibilities for building sugar houses. |
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Ah yes, "lump": the highly technical term which eluded me earlier. |
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The consensus in 2004 (see link) was that tetrahedral bricks wouldn't be that practical... |
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That's going to make for some sticky tabletop roleplaying games. |
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If a certain type of extinct bird were also to be fashioned out of sugar and perched on the geometric cube variation, would this be called a dododecahedron? |
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If a certain polyhedron could be made out of its excrement, would it be a dodododododecahedron? |
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Maybe yes, if he would do due diligence. |
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All of you, go seek help, while there's still time ...... |
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<resumes pumping up flamethrower> |
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It may turn out that dodecahedral lumps actually do dissolve faster. There are several transport phenomena to consider during a dissolution event. Material may dissolve from the surface (surface erosion), and if this is the only event, then cubes will dissolve faster due to their increased surface area. There is a second event, however, which entails the migration of solvent into the solid phase (in this case the water into the cube/dodecahedron) and the subsequent dissolution from the inside out (bulk dissolution). This second event may often be catalyzed by the dissolution products and may dominate the overall event; such is the case with many biodegradable polymers used in modern controlled release drug delivery devices. With this in mind, the question arises: Is solvent allowed into the interior void spaces of a sugar cube? |
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To test this theory, one may soak a cube in coffee for a matter of seconds, and then break the cube open along a cross section to observe solvent (coffee) penetration. It is clear upon observation that the solvent is allowed into the cube. |
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So, the final question follows thusly: is the crystalline sugar packed more tightly in a cube or a dodecahedron? If the answer is cube, which I will guess that it is (since crystalline sugar is basically cuboidal and so will fit more precisely without void spaces into a bulk cube) then this idea is not nearly in vain, as was initially assumed, since looser fitting crystals in a dodecahadron will allow faster bulk dissolution, increasing the rate of overall dissolution per unit volume. + |
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I was envisaging amorphous sugar, as it happens. I would expect it to be quite difficult to make sugar lumps of a radically different shape to the polyhedron in question. My original idea was to make it out of jaggery, but i didn't because i liked the idea of transparent or more saturated colours more than brownish ones. |
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Right. I can't believe i'm about to do this, but it is a Sunday and the clocks are going back. Tomorrow morning, i will go and buy a kilo of jaggery and set about it with a knife to carve different polyhedra from it, dunk them in hot water and time how long it takes each to dissolve. Anyone want to know the results? I'll weigh them first. |
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A thought - if you want it to dissolve faster, maybe it should be a [Menger sponge] (see link) instead? Although I guess the ultimate for faster dissolving would be powdered sugar rather than any sort of lump.
What about hollow or foamed sugar lumps that float?
Does crystallized sugar dissolve faster in some directions than others? If you could control the crystal-orientation, maybe you could make sugar balls that would spin as they dissolved? |
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A dodecahedral Menger sponge? That'll take a lot of whittling. On the other hand, maybe a freeze-drying approach would help.
I can visualise a cubical or tetrahedral Menger sponge, but i can't see an icosahedral or dodecahedral one. Maybe i'm just bad at visualising them, but i suspect they're impossible, regular ones anyway. |
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To improve solubility, make them hollow. A candyfab-style process may help in this regard (see link). |
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Incidentally, I claim prior art on the Menger sponge idea. There's a posting in the candyfab forums in the culinary applications topic by anon - which was me. For some reason I can't see it in the thread, but it's there as a popup in the recent forum posts list on the main page.
(actually I'd be surprised if I was the first to have thought of that!) |
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I too don't think you can have dodecahedral Menger sponges, since dodecahedra arn't space-filling. But that isn't what HughBothwell meant, anyway (he said 'instead'). |
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Apparently the jaggery lorry hasn't turned up! It'll have to wait.
[UnaBubba], yes, i had a go at making big crystals of sucrose once and they're sort of rhomboid-looking. I couldn't say exactly what symmetry class they fall into though. The answer, i'm pretty sure, is to use jaggery, since it's either cryptocrystalline or amorphous. However, for some reason the local (Muslim-run) cash and carry seems to respect the Christian sabbath, so i'm stuck here with no jaggery in the shops or anywhere else.
It seems there are Menger dodecahedra, though i still can't visualise them. See link.
How about an aerogel-style lump of sugar? |
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The image you linked to isn't convincing, ninteenthly. For one thing, the holes are different shapes. This isn't suprising since it isn't possible to tile regular pentagons. So you can't even make a pentagonal Sierpiñski carpet, let alone a 3D extension. |
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No, i know. That's what i meant by "sort of". I still think it might be possible with regularly irregularly spaced pentagons, or maybe in a non-Euclidean space, if you see what i mean.
In terms of its solubility, it would still work though, wouldn't it? |
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Just to say this. That Candyfab thing is just amazing! I want one! Sorry i didn't comment on it before, [Loris]. |
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I can't work out what it is, but i'm almost sure jaggery would work. I've carved the stuff myself, it doesn't seem to have a grain or any kind of visible cleavage planes, and it's got to be either amorphous or cryptocrystalline. It's not transparent, but may be susceptible to dyeing. |
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The candyfab thing does look great. I too want one, but not nearly enough to build it. |
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Hey, how did you get large sugar crystals, nineteenthly? |
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I tried to grow my own last year or so. The seed crystals grew okay, but when I dried to suspend one in a jar of solution on a piece of string it didn't get bigger - instead, I got a white lumps which started growing at the air:solution interface, then grew up the side and out the top. I had a cardboard lid with a few pinprick holes in, so this took quite some time. |
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My brother did it as a teenager before he left home but after i had, so i only saw the end results and i may have the details wrong. He simmered some water in a pan, then poured white sugar into it and dissolved it by constantly stirring until he reached the point where it couldn't take any more, then he poured it into jars and left them for, i think, several months. After a while, there were crystals all over the surface of the solution. I don't remember too clearly, but i think he also tied a knot in a string and hung it in the solution. I do remember the shapes being a long way from being isometric, but not clearly enough to tell you the symmetry. |
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Probably a good home ed project, now i come to think of it. |
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Anyway, i've got the jaggery now and will experiment with it shortly. That really does make a good home ed project. |
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Aggregation, maybe? How do they know when they are all together? I would hide in a corner to thwart the process. |
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[Unabubba], I will strive to make an opportunity to conduct that experiment with my engineering group. |
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I wager all the mechanical types would group rapidly, the software types eventually, and the electrical types would go into their own corners and hide. |
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Hmmm. That's pretty much exactly what I did. I mean the dissolving sugar in hot water, not getting kids to move around and hold hands. |
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So I put it down to the sucrose being mixed with contaminants like anti-caking agents, and forgot about it... |
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I spoke to him about it a couple of hours ago after my last anno, and he said that was what he did. However, it did take several months, apparently. |
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Heh, I've just fetched mine out. There's still liquid in the bottom, and the odd small real crystal - but mainly it's round white lumps round the rim, and fern-like sheets up the sides. Some sort of evaporative wick effect I imagine. |
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So I just had a thought, and tasted a bit... It's salt. :-)
Maybe sugar is easier, I'll try that now. I might also try different sorts of salt (that is - sea salt, rock salt etc) in case the aformentioned contaminants in table salt are what caused this result. |
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I remember why I started the project now actually. I'd found a bottle of NaCl (that is, 'salt') solution on my shelf in the lab with a cracked lid - over a period of several years it had formed the most gorgeous large crystals inside. |
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