z=m\lambda/4, \quad m = 1,3,5,\ldots”

in fact for electric field the heights should be

z =lambda/4 + m \lambda/2, \quad m = 1,2,3,\ldots

(the period is lambda/2 – not lambda/4)

]]>For non-platonic solids, the subtleties in the shape may affect how the die rolls, thus changing its fairness even though the facial area is the same. For instance, imagine a “fair” 3-sided coin: a disk of thickness r. Because the center of mass is closer to the face than to the edge, it’s easier for the coin to “roll” from edge to face than from face to edge when it hits the table and comes to a balance. Your triangular prism d5 has the same problem. Would it make sense to thicken the coin to compensate?

Similarly, I wonder about the “aspect ratio” of the trapezohedrons.

]]>I’m admittedly a dummy with respect to statistics but it looks like your d7 averages a roll of 3.958, and the expected average for a d7 would be 4, so it’s not biased too badly… ]]>

1. The Gamescience D7 you link to is probably the “Original” D7, dating to at least back into the 1980s.

2. Face-doubling: Many of the 1970s “D20s” were face-doubled 0-9 for use as percentiles and D10s, and you were expected to roll a D6 (for high/low or Odd/Even) to determine upper/lower, or ink the two sets of numbers differently. Similarly, the early runs of D30s were numbered -0 to -9/0-9/+0 to +9 for similar reasons.

3. There’s also face TRIPLING… Besides my D8-shaped D4s, I also have a D12-shaped D4 that is numbered I-IV (Roman numerals) three times.

]]>