Yes, rectangular parellelepiped works too. There are a bunch of other synonyms. You just need to be sure they're sufficiently qualified to restrict the faces to rectangles (and therefore the face angles to 90 degrees, and therefore the dihedral angles to 90 degrees). Regarding fair dice, I only trust solutions where all faces are geometrically identical to each other. For a 6-sided die, you can use a regular dodecahedron, with opposite faces having the same number (or in fact any other numbering with two of each of the numbers from one to six). For a 5-sided die, you can use a regular icosahedron with four of each number. An alternative strategy that works for even-numbers of six or higher is to use a bipyramind. This way you only need one face per number. Unfortunately, if the individual pyramids have odd numbers of faces (i.e., if the total number of faces is 2 mod 4), then you need to either read the result from the face on the bottom, or else paint the result on the exposed upper-edge. Or, you can double the number of faces and duplicate the numbers to avoid this problem. For odd numbers, you could of course use twice the number of faces with duplicate numbers. You could also use a pyramid with n sides, then use a rounded base that forces it to land on a side. You'd have to be very careful to make the base perfectly symmetrical to avoid biasing the direction in which it tips. I don't particularly like this solution, but you could always paint the values on the rounded part, avoiding the problem of having to read them from the edges in the odd case. A more elegant solution is to use curved sides, like the exposed surfaces of a peeled orange. Taper the ends and make them pointy (like an American football) so that it will always rest in the center of one of the sides. This will work for any number that's three or higher, although again, for an odd number of faces, you'd need to either read the answer from an edge or else double the number of faces. Tom Andy Latto writes:
On Wed, Jan 30, 2019 at 8:00 PM Fred Lunnon <fred.lunnon@gmail.com> wrote:
<< The word my father taught me for the three-dimensional analogue of a rectangle is "parallelopiped" >> I don't think so. See https://en.wikipedia.org/wiki/Parallelepiped
Which is presumably why I was taught "rectangular parallelepiped" as a child, which was fun to say, but certainly didn't achieve the goal of "a shorter and punchier word than 'rectangular solid' for this common concept!"
I suggest "oblong" is the word required.
But I've seen this used to refer to 2-dimensional as well as three-dimensional shapes, as well as to non-rectalinear shapes.
Andy
WFL
On 1/30/19, Mike Speciner <ms@alum.mit.edu> wrote:
Actually, it's parallelepiped.
On 30-Jan-19 18:19, Allan Wechsler wrote:
The word my father taught me for the three-dimensional analogue of a rectangle is "parallelopiped". Some author, I can't remember who, writes "2-box" and "3-box" and the like.
On Wed, Jan 30, 2019 at 6:07 PM Dan Asimov <dasimov@earthlink.net> wrote:
Good point!* I will now try to find if something comparable has been done for more general polyhedra.
—Dan
—————————————————————————————————————————————————————————————— * If you've never tried it, get a fat mass-market paperback (i.e., small format, c. 4"x7"), put a rubber band about it to hold it together, and note the disparate efforts needed in order to get it to spin 360º midair about the three axes perpendicular to the faces of this rectangular solid.**
** "Rectangular solid"??? Surely there is a shorter and punchier word for this common concept!
Andy Latto <andy.latto@pobox.com> écrit: ----- Assuming the die has 3 distinct moments, there are two stable ways to have the die spinning as it is tossed. I don't see any reason to expect the probabilities will be the same for these two different ways to throw the die. Or the unstable ways, but those are harder for the thrower to reproduce accurately. -----