I just got an e-mail, from Tumblr (I used to blog a lot there, before coming here to WordPress). The e-mail has the title, “Your Dashboard is literally on fire.” I’m now afraid to go look at my car, OR log on to my old Tumblr account. I dislike being burned.
I call the polyhedron above the rhombcuboctahedron. Other names for it are the rhombicuboctahedron (note the “i”), the small rhombcuboctahedron, and the small rhombicuboctahedron. Sometimes, the word “small,” when it appears, is put in parentheses. Of these multiple names, all of which I have seen in print, the second one given above is the most common, but I prefer to leave the “i” out, simply to make the word look and sound less like “rhombicosidodecahedron,” one of the polyhedra coming later in this post.
My preferred name for this polyhedron is the great rhombcuboctahedron, and it is also called the great rhombicuboctahedron. The only difference there is the “i,” and my reasoning for preferring the first name is the same as with its “little brother,” above. However, as with the first polyhedron in this post, the “i”-included version is more common than the name I prefer.
Unfortunately, this second polyhedron has another name, one I intensely dislike, but probably the most popular one of all — the truncated cuboctahedron. Johannes Kepler came up with this name, centuries ago, but there’s a big problem with it: if you truncate a cuboctahedron, you don’t get square faces where the truncated parts are removed. Instead, you get rectangles, and then have to deform the result to turn the rectangles into squares. Other names for this same polyhedron include the rhombitruncated cuboctahedron (given it by Magnus Wenninger) and the omnitruncated cube or cantitruncated cube (both of these names originated with Norman Johnson). My source for the named originators of these names is the Wikipedia article for this polyhedron, and, of course, the sources cited there.
This third polyhedron (which, incidentally, is the one of the thirteen Archimedean solids I find most attractive) is most commonly called the rhombicosidodecahedron. To my knowledge, no one intentionally leaves out the “i” after “rhomb-” in this name, and, for once, the most popular name is also the one I prefer. However, it also has a “big brother,” just like the polyhedron at the top of this post. For that reason, this polyhedron is sometimes called the small rhombicosidodecahedron, or even the (small) rhombicosidodecahedron, parentheses included.
I call this polyhedron the great rhombicosidodecahedron, and many others do as well — that is its second-most-popular name, and identifies it as the “big brother” of the third polyhedron shown in this post. Less frequently, you will find it referred to as the rhombitruncated icosidodecahedron (coined by Wenninger) or the omnitruncated dodecahedron or icosahedron (names given it by Johnson). Again, Wikipedia, and the sources cited there, are my sources for these attributions.
While I don’t use Wenninger’s nor Johnson’s names for this polyhedron, their terms for it don’t bother me, either, for they represent attempts to reduce confusion, rather than increase it. As with the second polyhedron shown above, this confusion started with Kepler, who, in his finite wisdom, called this polyhedron the truncated icosidodecahedron — a name which has “stuck” through the centuries, and is still its most popular name. However, it’s a bad name, unlike the others given it by Wenninger and Johnson. Here’s why: if you truncate an icosidodecahedron (just as with the truncation of a cuboctahedron, described in the commentary about the second polyhedron pictured above), you don’t get the square faces you see here. Instead, the squares come out of the truncation as rectangles, and then edge lengths must be adjusted in order to make all the faces regular, once more. I see that as cheating, and that’s why I wish the name “truncated icosidodecahedron,” along with “truncated cuboctahedron” for the great rhombcuboctahedron, would simply go away.
Here’s the last of the Archimedean solids with more than one English name:
Most who recognize this shape, including myself, call it the truncated cube. A few people, though, are extreme purists when it comes to Greek-derived words — worse than me, and I take that pretty far sometimes — and they won’t even call an ordinary (Platonic) cube a cube, preferring “hexahedron,” instead. These same people, predictably, call this Archimedean solid the truncated hexahedron. They are, technically, correct, I must admit. However, with the cube being, easily, the polyhedron most familiar to the general public, almost none of whom know, let alone use, the word “hexahedron,” this alternate term for the truncated cube will, I am certain, never gain much popularity.
It is unfortunate that five of the thirteen Archimedean solids have multiple names, for learning to spell and pronounce just one name for each of them would be task enough. Unlike in the field of chemistry, however, geometricians have no equivalent to the IUPAC (International Union of Pure and Applied Chemists), the folks who, among other things, select official, permanent names and symbols for newly-synthesized elements. For this reason, the multiple-name problem for certain polyhedra isn’t going away, any time soon.
(Image credit: a program called Stella 4d, available at www.software3d.com/Stella.php, was used to create all of the pictures in this post.)
Since I live in the American South, I hear a lot of talk about about sportsball. I have a hard time, though, telling exactly which variety of sportsball is being discussed. I don’t find sportsball interesting, and so I’m not fluent in any variant of sportsball jargon. For that reason, it can be difficult for me to tell which sportsballspeak-dialect is being used.
So, sometimes, just to try to make friendly conversation (while still being myself), I ask sportsball-fans questions, in order to find out which version they’re so intently discussing. (Figuring out why people obsessively talk about sportsball so much, I think, is a mystery I’ll never solve. Understanding the strange behavior of non-Aspies is much more difficult than the types of problems I enjoy trying to solve. As Albert Einstein said, when declining the presidency of Israel, “I have no head for human problems.”)
Here’s an example of one such question: “Are you talking about the type of sportsball often played inside, with a bunch of people chasing an orange sphere around on a wooden rectangle, and trying to get the sphere to pass through a metallic, elevated circle of slightly larger diameter than the sphere itself?”
Now, if someone mentions the sportsball game most people call “football,” there’s an obvious follow-up question that needs to be asked . . . so, of course, I ask it: “Which one?”
Replies to that question usually go something like this: “Whaddya mean, which one? Football! We’re talking about football, ya nerd!”
“But there are at least two games called by that name, which confuses me. Do you mean the sportsball-version where the players chase a prolate spheroid, or a rounded version of a truncated icosahedron?”
If they don’t understand that question, I attempt clarification: “You know, both those versions of sportsball are played on rectangles covered with grass . . . but the one with the prolate spheroid has two giant tuning forks at opposite sides end of the grassy rectangle, is usually played in the USA, and has a far higher rate of injuries, even fatal ones. The one that uses a truncated icosahedron doesn’t have tuning forks, is called ‘football’ by far more people than that American game, and isn’t nearly as dangerous. I think it’s at least a little more interesting than that other game people call ‘football,’ because of the Archimedean solid they chase around, since I like polyhedra. Which one are you discussing?”
If they tell me they’re talking about American football, I usually follow-up with a brief rant, for that sportsball-variant’s name confuses me. “Why do people call it that, anyway? I’ve seen it being play a few times — not for a full game, of course, but I can stand to watch it for a few minutes. That’s long enough to tell that the players only rarely use their feet to kick the prolate spheroid, and usually carry or throw it instead, using, of course, their hands. They usually use their feet just to run around chasing each other. Calling that version of sportsball by the term ‘football’ doesn’t make sense at all. In the game the rest of the world calls ‘football,’ the players kick the ball all the time, so I can understand why it has that name, but that prolate-spheroid version really should be called something else! Also, why are the games sometimes called ‘bowl games?’ They still play on a rectangle, and chase a prolate spheroid — there’s no actual bowl involved, is there?”
On occasion, they aren’t talking about any of these three varieties, though, but yet another form of sportsball. (Why are there so many?)
“Oh! You must mean the one played on a ninety-degree sector of a circle, with a square (confusingly called a ‘diamond,’ for some reason) in its interior, positioned such that one of its vertices is at the circle’s center. At that vertex, there’s a convex-but-still-irregular pentagon on the ground, while the other three vertices of the large, grass-covered square have much smaller squares on the ground, instead of a pentagon. The guy standing at the pentagon is always trying to hit a red-and-white sphere with a wooden or aluminum stick, but he usually misses. The guy who throws the sphere toward the region above that pentagon usually scratches himself, and spits — a lot. He must be important in some way, for he’s provided with a small hill to stand on, literally placing him above the rest of the players. Have I got it now?”
Sometimes, people try to get me to stop calling these strange activities “sportsball,” by bringing up hockey as an objection. “You can’t call all sports ‘sportsball!’ What about hockey? It doesn’t even have ball! It’s got a puck!”
I’m always ready for this objection, though. “You mean the one with the short black cylinder that slides across ice? That’s a sport? I thought it was just an excuse to have fights!”
These polygons are known to virtually all speakers of English as the triangle and the quadrilateral, but that doesn’t mean I have to like that fact, and, the truth is, I don’t. Why? There are a couple of reasons, all involving lack of consistency with the established names of other polygons.
Consider the names of the next few polygons, as the number of sides increases: the pentagon, hexagon, heptagon, and octagon. The “-gon” suffix refers to the corners, or angles, of these figures, and is derived from Greek, The end of the word “triangle” also refers to the same thing — but not in Greek. For the sake of consistency, triangles should, instead, be called “trigons.”
In the case of the quadrilateral, the problem is twofold. The suffix “-lateral” refers to sides, not angles. For the sake of consistency, “-gon” should be used instead. The prefix “quadri-” does mean four, of course, but is derived from Latin, not Greek. We use the Greek prefix “tetra-” to refer to four when naming polyhedra (“tetrahedron”), so why not use it for polygons with four sides, also? The best name available for four-sided polygons requires a change in both the prefix and suffix of the word, resulting in the name “tetragon” for the figure on the right.
When I listed the names of higher polygons above, I deliberately stopped with the octagon. Here’s the next polygon, with nine sides and angles:
I’m guilty of inconsistency with the name of nine-sided polygons, myself. All over this blog, you can find references to “nonagons,” and the prefix “nona-” is derived from Latin. Those who already know better have, for years, been calling nine-sided polygons “enneagons,” using the Greek prefix for nine, rather than the Latin prefix, for reasons of consistency. I’m not going to go to the trouble to go back and edit every previous post on this blog to change “nonagon” to “enneagon,” at least right now, but, in future posts, I will join those who use “enneagon.”
Here’s one more, with eleven sides:
I don’t remember ever blogging about polygons with eleven sides, but I have told geometry students, in the past, that they are called “undecagons.” I won’t make that mistake again, for the derivation of that word, as is the case with “nonagon,” uses both Latin and Greek. A better name for the same figure, already in use, is “hendecagon,” and I’m joining the ranks of those who use that term, derived purely from Greek, effective immediately.
With “hendecagon” and “enneagon,” I don’t think use of these better names will cause confusion, given that they are already used with considerable frequency. Unfortunately, that’s not the case with the little-used, relatively-unknown words “trigon” and “tetragon,” so I’ll still be using those more-familiar names I don’t like, just to avoid being asked “What’s a trigon?” or “What’s a tetragon?” repeatedly, for three- and four-sided polygons. Sometimes, I must concede, it is necessary to choose the lesser of two irritations. With “triangle” and “quadrilateral,” this is one of those times.
A vacuum is, by definition, a region of space devoid of matter. While a perfect vacuum is a physical impossibility, very good approximations exist. Interplanetary space is good, especially far from the sun. Interstellar space is better, and intergalactic space is even better than that.
Along come humans, then, and they invent these things:
. . . and call them “vacuum cleaners.”
Now, this makes absolutely no sense. There isn’t anything cleaner than a vacuum — and the closer to an ideal vacuum a real vacuum comes, the cleaner it gets. Since vacuums are the cleanest regions of space around already, why would anyone pay good money for a machine that supposedly cleans them? They’re already clean!
Even cleaning in general is a puzzle, without vacuums being involved at all. To attempt to clean something — anything — is, by definition, an attempt to fight the Second Law of Thermodynamics. Isn’t it obvious that any such effort is, in the long run, doomed from the outset?
—–
[Image note: I didn’t create the images for this post, but found them using Google. I assume they are in the public domain.]
Source for quote: https://en.wikipedia.org/wiki/Portal:Mathematics
Regions between close-packed circles of equal radius resemble triangles, but with 60 degree arcs replacing the sides. As these regions are the only things left of a plane after all such circles are sliced out, and they each are outside all the circles used, I’ve decided to name them “circumslices.” Interestingly, the three interior angles of a circumslice each asymptotically approach zero degrees, as one approaches circumslice-vertices, which are also the points of contact of the circles.
Why did I name these things “circumslices?” Because they needed a name, that’s why!
Aspies (a term for ourselves, used by those with diagnosed or undiagnosed Asperger’s) sometimes have trouble understanding what people say, because we tend to view things literally, while many others often say things in non-literal, or even anti-literal, ways.
For example, without reasons known to us, person A says something offensive to person B. Why deliberately offend someone, without good cause? We don’t know. Person B then says, in response, “Say that again!” — and Aspies who hear this (and we do, for we’re everywhere) often become even more confused. Clearly, person B does not actually want to be offended again, yet is telling person A to do exactly that which person B does not really want person A to do. I’ve asked people to explain this behavior more than once, tried to understand it, and each time I revisit the subject, I become more confused than before, for understanding the explanation would involve bending my mind in a direction it simply won’t bend. I also must admit I do not want my mind to bend that direction, either, for fear that doing so would weaken my ability to reason logically.
This is true for much of what I hear. Things that do not make logical sense are inherently hard to understand, at least for us . . . and I don’t even understand why everyone isn’t like us in this respect, either.
Of all the signs used to advertise strip clubs, the one that is most familiar, and most recognizable, is the type you see here — just one I picked, of many like it, from the results of a Google image-search.
It’s also mathematically inaccurate. “Girls” are, by definition, human female children. Any strip club, in any developed country, that actually had real girls stripping would quickly be closed down by the authorities, and rightly so. Where I live (Arkansas, in the USA), strip clubs do not hire performers who are younger than age 18, and that means that, legally, these strippers are adults.
Adult human females are, of course, properly called “women,” not “girls.” Therefore, these signs, seen on strip clubs all over the place, should actually say “WOMEN WOMEN WOMEN,” not “GIRLS GIRLS GIRLS.”
This may not be what most other people think about when they’re driving around, and see strip club advertising, but both mathematical and linguistic inaccuracy bother me — a lot.
I have actually heard two different high school principals say, to assembled students in one case, and a faculty meeting in the other, that “mediocracy” was not acceptable, nor what we should want as a school, from our students, blah blah blah. Use a non-word like that, and you’ve lost me as a listener, possibly permanently.
Clearly, the fact that two different principals (neither at my current school, by the way) in central Arkansas did this same SNAFU means it is likely that someone nearby is teaching this to people, spreading the idea to replace “mediocrity” (a perfectly good word) with “mediocracy.” They’re probably doing this at a nearby teacher school, er, I mean, “College of Education.”
This got me wondering about possible definitions for “mediocracy.” One comes to mind very quickly, and that is a system of government: rule by the mediocre.
Oh, wait, we have that already, and have had it for as long as I can remember. I guess we are willing to accept mediocracy, at the federal, state, and local levels, and in all branches of government.
Sigh.
RobertLovesPi.net 