Initial Die Calculation Results.

The calculation of the Mass Properties would be very cumbersome and lengthy to perform by hand so I resorted to using a 3D Solid Modeling Application. The results show that the center-of-mass is slightly off-center. My die was modeled to be 50[in] on each side and made of polycarbonate. I used the large size in order to obtain results that made sense (the results using 0.5[in] die were not meaningful). By increasing the size by 100x I achieved readable results. Of course I made corrections in the results to bring it back to the scale of 0.5[in]. The mass was reduced by 10^6, linear values reduced by 10^2 and Mass Moments of Inertia by 10^10.



The die center-of-mass is:
- shifted 0.00065[in] away from the "six" and toward the "one",
- shifted 0.00039[in] away from the "five" and toward the "two" and
- shifted 0.00013[in] away from the "four" and toward the "three".

The greater the difference in the number of dots, the greater the shift was away from the face with the greater number.

The spinning axis would be determined by using the directions and magnitudes on the Mass-Moments-of-Inertia. I will have to determine how to read the results but I suspect the following:

- The axis will extend from the "four" face near the corner by "five" and "six" to - The "one" face near the corner by "two" and "three".

This would possibly result in a greater probability of a spinning die to come to rest on one of the two faces that the axis intersects. Pending a clear interpretation of the calculations, I believe these faces are the "one" and the "four". Furthermore, since the greatest shift in the center of mass was toward the "one" face I predict the greater probability of rolling a "six" than any other number. Note: The "six" face is opposite the "one" face which is also the "heaviest".

If you can help in the interpretation then we can make a more refined prediction.

Based on my assessment so far, there is ever so slightly greater chance of rolling a "six" than any other number.

But, Hey! Does it really matter?

I will be making a list of ideas to pursue. Comments or suggestions are welcome.

Irasohn