Three Polyhedra Which Resemble Caltrops

Caltrops, when resting on a horizontal surface, have a sharp, narrow point sticking straight up. Stepping on such objects is painful. Most polyhedra do not have such a shape; the most well-known example of an exception to this is the tetrahedron. This fact is well-known to many players of role-playing games, who often use the term “d4” for tetrahedral dice, and who usually try to avoid stepping on them. Here are some other polyhedra which resemble caltrops. All were made using Stella 4d, software available at this website. The first two images may be made larger by simply clicking on them.

The third example, made with the same program, varies this idea somewhat: in physical form, resting on a floor, this caltrop-polyhedron would have three, not just one, potentially foot-damaging “spikes” sticking straight up.

12-pointed caltrop


The Misadventures of Jynx the Kitten, Chapter Two: Jynx vs. My Computer

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Jynx: 1, Computer: 0.

Tonight’s feline insanity started while we were watching Star Trek — the episode where Captain Kirk and Mr. Spock go up against a planet full of nuclear-armed Space Nazis.

Apparently, cats — or, at least, this cat — find Nazis disturbing, which, of course, they were — and will be again, if they appear in the 23rd Century . . . because some half-crazed future historian went and violated the Prime Directive, becoming, a few years later, a fully-crazed future historian. Jynx was so incredibly disturbed by the Space Nazis, in fact, that he bounced over pillows and blankets, in a series of nicely Newtonian . . .

&^ (Stop that, Jynx!)

. . . parabolic arcs, to land on my computer. He then proceeded to pause the episode — then close my browser (the picture-moment, with my wife laughing hysterically as she took it), and finally tried to bite the heads off several Space Nazis as the screen slowly darkened. After due consideration, Jynx decided this was not enough, and so, next, he reached out a paw, and quickly turned my computer completely off. A smug look followed. You haven’t seen a look this smug, unless, maybe, you’ve also seen one on the face of a kitten.

Getting it (my computer, not Jynx) turned back on was not easy. For a little while, in fact, I thought Jynx had destroyed the Internet. In reality, the Internet had been fine all along, for this picture, taken a little earlier, with a tablet, got to my e-mail account almost instantly. It took much longer, however, for me to actually get to my e-mail account.

My computer now has tiny bite marks all over it, and plays Radiohead’s song “2 + 2 = 5” so slowly that it’s turned the song into “1.5 + 1.5 = π” – and that song sounds terrible.

I hope my computer lives long enough for this post to make it to my blog. In the meantime, Jynx reigns — OW! — triumphant.

[2016 update: that computer is now officially dead. Jynx the Cat lives on.]

The Pain Is Gone (but not without cost)

Every day for almost 25 years, my vertebrae from mid-neck to torso have been jammed together, by a fall I had at age 20. It hurt like hell, at times, or it just hurt, but it never, ever stopped completely, until all of this happened.

Eyes closed, I attacked the pain as if it were an inanimate thing, laying backward on the corner of the mattress with the one point of contact being a bit above the spot between my shoulder blades, centered horizontally West-East, while facing North. It moved to the left. I followed, pursuing it — and then we shifted to it and me stretching myself in opposite directions, then with the forces in the same direction again, then the reverse again, with this cycle repeated many times.

Pain, my enemy, then made a rapid jump to an entirely new quadrant. The focus line of movement, in reaction, shifted at my center of mass. I rotated by a right angle counter-clockwise, and was now facing West with my hands on a line South-North, lined up with my shoulders. I pointed my fingers up-down and stretched that way as well, and had therefore identified three mutually perpendicular directions, in each case coming up with some way to reverse the direction of force (having my arms both curled tightly in front of my face and beyond, in the second case, and then touching my toes and holding them for the reversal of up-down.

At that point, I stood straight up. I was shocked. I still am. This hasn’t worn off, as I write this. As long as I stand straight up — but only then — the pain is gone.

Gone.  And that damned thing had me going to doctors and chiropractors for years.  Gone, just like that.  I had no idea this would result from my spontaneous and protracted, intense exercise session, but it did.

If I slouch in any way, though, I get immediate and intense pain, which quickly trained me to stand and sit up straight. I don’t know, yet, how or if sleep will work, and haven’t tested the perfectly horizontal. If I want anything more casual than full attention, I have to tolerate pain for as long as the deviation persists, pain with intensity proportional to the deviation.

I’ve created my own Skinner Box, although I didn’t realize that was what I was doing. I can lie in it, but I wonder if I can sleep in it?

I don’t recommend trying this yourself, unless you first consult with, and obtain the approval of, a physician. Further updates as events warrant.