Sources page biographical material

5.AF. SPOTTING DICE
New section. In the early 1980s, I asked Richard Guy what was the 'standard' configuration for a die and later asked Ray Bathke if he used a standard pattern. Assuming opposite sides add to seven there are two handednesses. But also the spot pattern of the two, three and six has two orientations, giving 16 different patterns of die. Ray said that when he furnished dice with games, some customers had sent them back because they weren't the same. Within about three years, I had obtained examples of all sixteen patterns! Indeed, I often found several patterns in a single batch from one manufacturer. Ray Bathke also pointed out that the small dice that come from the oriental games have the two arranged either horizontally or vertically rather than diagonally, giving another 16 patterns. I have only obtained five of these, but with both handednesses included. I used this idea in one of my Brain Twisters, cf below.

Since the 2, 3 and 6 faces all meet at a corner, one has just to describe this corner. The 2, 3, 6 can be clockwise around the corner or anti-clockwise. Note that 236 is clockwise if and only if 132 is clockwise. The position of the 2 and 3 can be described by saying whether the pattern points toward or away from the corner. If we place the 2 upward, then 6 will be a vertical face and we can describe it by saying whether the lines of three spots are vertical or horizontal. Guy told me a system for describing a die, but it's not in Winning Ways and I've forgotten it, so I'll invent my own.

We write the sequence 236 if 236 is arranged clockwise at the 236 corner and we write 263 otherwise. When looked at cornerwise, with the 2 on top, the pattern of the 2 may appear vertical or horizontal. We write 2 when it is vertical and 2 when it is horizontal. (For oriental dice, the 2 will appear on a diagonal and can be indicated by 2 or 2. If we now rotate the cube to bring the 3 on top, its pattern will appear either vertical or horizontal and we write 3 or 3. Putting the 2 back on top, the 6 face will be upright and the lines of three spots will be either vertical or horizontal, which we denote by 6 or 6.
David Singmaster. Dicing around. Weekend Telegraph (16 Dec 1989). = Games & Puzzles No. 15 (Jun 1995) 22-23 & 16 (Jul 1995) 43-44. How many dice are there? Describes the normal 16 and mentions the other 16.

Ian Stewart. The lore and lure of dice. SA (Nov 1997) ??. He asserts that the standard pattern has 132 going clockwise at a corner, except that the Japanese use the mirror-image version in playing mah-jongg. His picture has both 2 and 3 toward the 236 corner and the 6 being vertical, i.e. in pattern 236. He discusses crooked dice of various sorts and that the only way to make all values from 1 to 12 equally likely is to have 123456 on one die and 000666 on the other.

Ricky Jay. The story of dice. The New Yorker (11 Dec 2000) 90-95.