I am in the process of modeling dice for my board game to create customized 3, 4, 5, 7, 8, 9, 10, 11 and 12 sided dice. I have access to a 3D printer, so I planned on 3D printing these models once they are finished.
I would like to create dice with the fairest probabilities, so see linked image below for example of the style I like: (this example is of a 9-sided dice) https://upload.wikimedia.org/wikipedia/commons/3/3d/D9_dice.JPG
As you can see, it's mostly a spherical shape but with evenly spaced holes cut out of it. Now, for those of you not familiar with modeling, I have an option to "cut" out shapes using a process called a Boolean operation. If you are familiar with what a Moravian star looks like, imagine all the points of that type of star is instead just a single line/axis. I can then create a cylinder around those axes to populate the shape I need to apply a boolean to the sphere to "cut out" the holes. In order for me to accurately "cut out" these holes in the sphere, I need to be able to accurately calculate the correct positioning of each of these "axises" in the 3D workspace (x, y and z coordinates) for all types of dice (3-12 sides) so that they are evenly spaced out around the sphere's edge. So, for example, if I was making a 9 sided dice like shown in the image link above, I would need to have 9 axises all fixated around a center point - the center point would be the center point of the sphere in this case. The length of the axes can be a fixed value because it doesn't really matter since I am just using it to create the correct angles to populate the cylinders to do a boolean action to the sphere to cut out holes.
Since this is the case, I need to figure out the rotational value of all the axis for this 9-sided dice:
9-Sided Dice Axis Rotations:
- Axis 1 will always be at x: 0° | y: 0° |z: 0°
- Axis 2 = x: ?° | y: ?° | z: ?°
- Axis 3 = x: ?° | y: ?° | z: ?°
- Axis 4 = x: ?° | y: ?° | z: ?°
- Axis 5 = x: ?° | y: ?° | z: ?°
- Axis 6 = x: ?° | y: ?° | z: ?°
- Axis 7 = x: ?° | y: ?° | z: ?°
- Axis 8 = x: ?° | y: ?° | z: ?°
- Axis 9 = x: ?° | y: ?° | z: ?°
If you could help me figure out the kind of math I need to do here since I'll have to do the same math for D3, D4, D5, D7, D8, D9, D10, D11 and D12 sided dice, I would be most grateful. Now, I'm a firm believer of leading a horse to water, but if you wanted to be overly helpful, and you wanted to do the math for me for all dice....well....you'd be just alright, my friend. ;)
In all seriousness, thank you for your time and response(s)!
~Jared
PS: the 3D modeling software I am using is Blender if you were curious. If you know how to answer my question using methods in Blender, please post your answer in my question in the blender forums found here!