Date: 2008-02-10 15:41:00
date cubes
A while ago I came across a desk calendar where the day of the month was represented by two cubes with digits on them. By arranging the cubes the right way, one can represent any day of the month from 01 to 31. It turns out that there are essentially two ways to do this, depending on whether you want to represent dates before the 10th as "05" with a leading zero or "5" without.

If you don't want the leading zero, then you only need the digit 0 on one of the cubes so you can represent 10, 20, and 30. Create one cube with (1,2,3,4,5,6) and the other with (0,1,2,7,8,9) and you can represent any date from 1 to 31 (well, really 32).

If you do want the leading zero, you need to have a 0 on both cubes to represent each date from 01 through 09. However, this presents a problem: You need 0, 1, and 2 on each cube, but that only leaves room for six more digits, and there are seven left to place (3 through 9). The trick is to note that 6 and 9 look pretty much the same when turned upside down, so you can omit one of them and turn the cube over to represent either one. So, you have cubes with (0,1,2,3,4,5) and (0,1,2,6,7,8).

Because I lack the woodworking tools to make a nice set of date cubes out of something durable like wood, I opted for something a bit less durable: Paper plus inkjet printer. I also took this as an opportunity to learn something about creating Postscript by hand (it's not that bad really), and came up with datecubes.ps which you can print, cut out, fold, and paste together. If you're on a Mac, then the Preview app can handle Postscript files natively, otherwise you'll have to use something like GSview to print/view it.

Update: I'm feeling nice so I made a datecubes.pdf for anybody who finds plain Postscript files awkward to deal with.

2008-02-10T03:28:48Z
Create one cube with (1,2,3,4,5,6) and the other with (0,1,2,7,8,9) and you can represent any date from 1 to 31 (well, really 32).

The FAA must use these; it would explain a lot.

2008-02-10T07:27:31Z
If you don't want the leading zero, then you only need the digit 0 on one of the cubes so you can represent 10, 20, and 30. Create one cube with (1,2,3,4,5,6) and the other with (0,1,2,7,8,9) and you can represent any date from 1 to 31 (well, really 32).

This seems like a cheat to me. Those calendars (that I've seen, anyway) have a slot where you put the 2 cubes. So with your design for the 2 cubes, you can't actually show single digit numbers, since none of your faces are blank. So your solution requires one to hide one of the cubes somewhere else for the first third of the month, which seems inconvenient and silly. Please correct this bug. [Severity: High. Priority: High.]

2008-02-10T08:40:45Z
Suggested resolutions:

1. Represent the day of the month in base 6, so the cubes can be (blank,1,2,3,4,5) and (0,1,2,3,4,5).

2. Construct two tesseracts which can each be rotated in 4-space to expose eight different cubes in 3-space. Labeling the faces of the tesseracts is left as an exercise for the reader.

3. Upgrade from cubes to regular octahedrons. The faces can then be (blank,0,1,2,3,4,5,6) and (blank,0,1,2,7,8,9,x) where the face labeled x is unused.

4. Upgrade from cubes to regular dodecahedrons. The faces can then be (blank,1,2,3,4,5,6,7,8,9,x,x) and (0,1,2,3,4,5,6,7,8,9,x,x) where faces labeled x are unused. This proposal has the additional benefit that the names of the month can also be labeled on a third dodecahedron, preserving symmetry.

5. Reduce the number of days in a month to a maximum of 21. Label the cubes (blank,1,2,3,4,5) and (blank,0,1,6,7,8) (recalling that 6 can also be used to represent 9). Unfortunately I was unable to find a compatible calendar on the Calendar Reform page, so one must be constructed.

6. Various physical means may be employed such as using an arrangement of polarizing filters and internal illumination to make the left hand digit disappear from view if the cube is rotated so the digit on the front face is oriented 90° from vertical.

7. Arrange the tray in which the cubes sit so that it may be easily rotated through 90° around a vertical axis, thus hiding one cube behind the other when viewed from the front.

2008-02-10T09:28:07Z
Resolved.
Greg Hewgill <greg@hewgill.com>