This a a die I designed a long time ago and that I forgot numbering.
So, after a long time on the drawing table, here is the
D18 Sphere:
As the number of faces is even, each number is exactly on a face (sometimes, these dice look very usual
).
Instead, the numbering is very interesting in this case.
Opposite faces numbers sum to 19, obviously. As a consequence any group of 8 numbers of a large diameter sum to 76. A more unexpected consequence is that any group of 5 numbers follows this strange rule: if you sum the double of the central number to the 4 other surrounding numbers, you obtain 57.
Example in the rendering image:
...4..
9 18 5
...3..
2x18 + 4 + 9 + 5 + 3 = 57
But the most interesting property in this particular numbering is that the sum of the six numbers surrounding a spherical zone is always 57.
Example here: 18 + 5 + 7 + 11 +13 + 3 = 57
I had to use a computer to find the good combination (there are a lot of them, by the way).
I could number this die from 1 to 9 twice (I found a way of doing it where the 8 numbers of the large diameters always sum to 40) or from 1 to 6 three time or even from 1 to 3 six times. Let me know if you want some particular numbering.