Calendar Dice and related designs
The form of dice have been with us since antiquity. The traditional die with six sides, numbered one through six, is what most people are familiar with, although eight-, twelve-, and twenty-sided dice are often used in various games involving different permutations of chance.
The six-sided dicehas a total of twenty-one spots, a number that I believe the late author, Douglas Adams, in his Restaurant at the End of the Universe (from the Hitch-hiker’s Guide to the Galaxy series) had in mind when conceiving “the Ultimate Answer to the Ultimate Question” posed by the computer ‘Deep Thought’ at the end of the book. The answer, “Forty Two” was arrived at after centuries and millennia of calculations. Does this not correspond to the number of spots on a pair of dice?
The form I had arrived at in the calendar dice is a little more abstracted, relying as it does on an understanding of the three-dimensional structure of the die, made to resemble the form which excludes the spots. The six-sided die is a hollow form, based on a cube of 9 x 9 x 9 smaller cubes. If we hollow this form out to leave a shell, and subtract the cubes where the spots would be, we have:
729 cubes - 343 cubes - 21 cubes = 365 cubes
which is the length of a standard Solar Year in the Western Calendar system. In addition, a dice form constructed from the geometric opposite of the cube, the eight-sided octahedron, will, surprisingly, give us a hollow shell comprising 366 units. The geometry is constructed using hexagonal close-packed spheres, rather than stacked cubes. An octahedron with an edge of eleven units (spheres) is made hollow, much as the cube, by subtracting the interior form with an edge of nine units, and further subtracted by the thirty-six spots that we see on an eight sided die, numbered one through eight:
891 spheres - 489 spheres - 36 spheres = 366 spheres
It is interesting to note that the scales of the two objects match precisely when constructed of cubes and spheres with identical edge or diameter measurements.