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

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

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Are you familiar with this one: dicecollector.com/… – wax eagle Jan 31 '14 at 22:15
I think this might have better luck at Math.SE. – SevenSidedDie Feb 1 '14 at 0:46
This shape seems like it would minimize roll distance: thediceshoponline.com/dice/4511/… – Mooing Duck Sep 25 '14 at 21:18

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.

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I like this idea, I didn't even think about rearranging the values. I'll have to look into this more and play around a bit. – AdamSpurgin Feb 1 '14 at 3:27
Might be easier to put the geometric symbols on the outer side of the numbers than around them. That in turn means no elimination necessary: every number just has 1-3 symbols beside it. – doppelgreener Feb 1 '14 at 3:32
I got this figured out and your suggestion was by far the most helpful. I've started plotting out the design, and it goes a little something like this: i.imgur.com/A06KydS.jpg . How it works: roll the die, if the shape at either corner of the face represents the die you want, read the bottom number, otherwise read the top. – AdamSpurgin Feb 2 '14 at 9:53
Glad you like! I like the shapes on the corners way better than my idea. Two concerns with this design - how will those shapes look on a printed die? Does the detail show up or will they all look like dots? Also, will two digits fit on the 10, 11, and 12 faces? – valadil Feb 3 '14 at 1:02
Not sure how much more fiddling this needs, but I noticed that you can reduce it to only 4 faces with 2 pairs if you replace row 5 with (1 5 5 5) and row 13 with (1 1 5 1), and replace row 6 with (2 2 6 2) and row 14 with (2 6 6 6). – Zimul8r Feb 3 '14 at 14:23

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

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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
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This looks like it would take more detail than just putting all the numbers on it, which isn't feasible. – AdamSpurgin Jan 31 '14 at 23:57
And unless you have very good color vision, it's going to be damnably difficult to distinguish between black and colored lines at that level of size and clutter. But it is a supremely clever way of incorporating the information. – KRyan Feb 1 '14 at 1:19

(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.

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