Coming up with a numbering system for an 'omni-die'

Question

I'm trying to design an 'omni-die' of sorts. A d24 numbered such that it can be read as a d4, d6, d8, and d12. My problem is this: how do I fit 4 number's worth of information on the very small face of the die? putting all the numbers, or really more than 1, wouldn't work, I can't get that level of detail.

The information I want on each face is as follows:

 1: 1 1 1 1 
 2: 2 2 2 2
 3: 3 3 3 3
 4: 4 4 4 4
 5: 1 5 5 5
 6: 2 6 6 6
 7: 3 1 7 7
 8: 4 2 8 8
 9: 1 3 1 9
10: 2 4 2 10
11: 3 5 3 11
12: 4 6 4 12
13: 1 1 5 1
14: 2 2 6 2
15: 3 3 7 3
16: 4 4 8 4
17: 1 5 1 5
18: 2 6 2 6
19: 3 1 3 7
20: 4 2 4 8
21: 1 3 5 9
22: 2 4 6 10
23: 3 5 7 11
24: 4 6 8 12

d4 and d8 are easy enough, they are both exponents of a common base(2). I can use simple symbols to represent a binary number and disregard the most significant bit when reading it as a d4. e.g.

001 : 1 --> _01 : 1
110 : 6 --> _10 : 2
111 : 7 --> _11 : 3
000 : 8 --> _00 : 4

but d6 and d12 don't really fit as well. I could use a ternary number system, but then it starts getting cluttered. Any thoughts? or better yet, has anyone seen this made before and know where I can buy one?

edit: this is my plan for the geometry, aiming for 1" tall

Answer 1

I lied in my comment. I still came up with a schema. Instead of using the numbers you listed at first, use them in this order:

d4  d6  d8  d12
1   5   1   1
2   6   2   2
3   5   3   3
4   6   4   4
1   1   5   5
2   2   6   6
3   3   7   7
4   4   8   8
1   1   1   9
2   2   2   10
3   3   3   11
4   4   4   12
1   5   5   1
2   6   6   2
3   3   7   3
4   4   8   4
3   5   5   5
4   6   6   6
1   1   7   7
2   2   8   8
1   1   1   9
2   2   2   10
3   3   3   11
4   4   4   12

This asserts that you always have one or two numbers per face, which is way more likely to fit. Now all it needs is notation to indicate which die uses which value.

My suggestion is with an outline. I'd shape it roughly like the die it's for. When a d4 has a unique value on a face, surround it with a triangle. d6 gets a square, d8 an octagon. I'd just give the d12 a circle for simplicity's sake. The values with no outline belong to the other three dice by process of elimination.

I tried to arrange things so there was exactly one unique value on each face, but I couldn't pull it off. Maybe a double outline in that case? This affects 6 faces.

(Also, someone should check that this does what I say it does. I'm tired enough that I'd be shocked if I didn't overlook a number somewhere. I did test that each column averages out to the expected value.

Answer 2

If you don't mind a little bit of math, you could just label the sides from 1 to 24. To roll a dN where 24 is divisible by N (i.e. 2, 3, 4, 6, 8, 12) read the number rolled modulo N (divide and take the remainder). You will want to use N instead of 0 if the result divides N exactly.

For example, rolling a 10 would be interpreted as:
2 on a d2 (10 mod 2 = 0)
1 on a d3 (10 mod 3 = 1)
2 on a d4
4 on a d6
2 on a d8
10 on a d12

Answer 3

(If) some coloring variation and minor math are acceptable to interpret the result, you could do it this way (without any division or rounding). Also, you pick up a d3 'for free'

Make the top 1/2 of the die black with white lettering, bottom half white with black lettering as shown in my chart below. Both halves have the same numbers on their faces. To get back to 12 distinct numbers in base10 take (3 × first digit) + 2nd digit. So 23 = (2×3) + 3 = 9 for example.

• To roll as a d24, take the number back to base10 and add 12 if black
• To roll as a d12, take the number back to base10 (don't care, white or black)
• To roll as a d8, take the 1st digit on the face, add 1 and add another 4 if black
• To roll as a d6, take the 2nd digit on the face and add 3 if black
• To roll as a d4 take the 1st digit on the face and add 1 (don't care, white or black)
• To roll as a d3, just take the 2nd digit on the face (don't care, white or black)

*Note, the actual numbers on the die face aren't really base3 or base4, you'll notice my 2nd digit never has a zero, but it seems to work this way.

If color variation doesn't work for your production method, you could also do it by some kind of 'pip' or underlining of the number so you knew which was the top 1/2 and which was the bottom. Actually that kind of thing might be good for those 2 unused 'cone tops' in your die model that aren't actually number faces - you could denote it once there on each top, so you knew whether you were in 'black' or 'white' mode.

Answer 4

This represents what one face of such a die might look like. The black lines would either be very faint or missing entirely. The number of colored/visible faces represent the value in that die's base. Since there are 3 points colored on the star, rolling this would be a 3 in base 12. Likewise for the square (base 4), hexagon (base 6), and octagon (base 8). For base 24, you simply put the number itself.

This monochromatic alternative shows all 24 faces and uses alternating hollow/solid dots. The faces shown are faces of a regular 24-sided polyhedron (an icosikaitetragon).

1. d4: count large solid dots. If there are none, count the large hollow dots.
2. d6: count small solid dots. If there are none, count the small hollow dots.
3. d8: count large solid dots twice, and large hollow dots once.
4. d12: count small solid dots twice, and small hollow dots once.
5. d24: use central numeral