More on sevensided dice

Several years ago I made some seven-sided dice for some medieval board games mentioned in the Libre de los Juegos (1283) by Alphonso X 'The Wise'. These dice were not entirely fair, as they showed more often the 6 and 7 on the pentagon sides. As I now had some spare antler (from the reconstructed Noyon chess pieces), it was time to create some better dice.

The old seven-sided dice.

First, a large pentagon column was made having equal sides at a 72 degree angle. Then, the idea was that the pentagon and the rectangles should have the same surface area. If you have the length of one side of the pentagon, this is easily calculated using the next formula. Or even easier, you can use a website to do this for you. From the surface area you then can calculate the length of the rectangle, as a of the pentagon and a of the rectangle are the same, as well as the surface A.

The pentagon and the formula for the surface area (A).

 The rectangle and the formula for the surface area (A).

Funny enough this did not yield a fair dice. On the contrary, here, most of times the rectangles showed. If you reconsider this, it is logical, as the edges of the dice are not the same: 72 versus 90 degrees. What followed next was a careful shortening of the rectangles with a belt sander, and checking whether the dice throw (>200 throws) became fair. In the end, after several removal steps, I now have reasonably fair seven-sided dice.

The new seven-sided dice.