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Does anyone know the exact proportions of a face of the d10? I'm…
2nd-Apr-2005 09:28 am
Does anyone know the exact proportions of a face of the d10? I'm trying to program mathematical models of the dice.
2nd-Apr-2005 08:37 pm (UTC)
I did some poking around and couldn't find it. There is a bit of a trick (or two) to make them because it is not composed of equal-sided shapes. So then I tried to see if I could figure it out. My geometry isn't the best, so I couldn't figure it out using pure math. I tried a few different methods, including using a CAD program. I couldn't quite get it to work out. Finally I got tired of playing with it.

I started by grabbing a physical image of some dice. I pulled it into PhotoShop and grabbed some rough dimensions of one side. Then I tried re-creating the side on paper to figure out real dimensions/ratios/angles. I thought I had it, but when I pulled it into a CAD program and created it, it would never quite work out.

http://www.enchantedlearning.com/dictionarysubjects/math.shtml
http://www.enchantedlearning.com/math/geometry/solids/

The image of real/physical dice I used:
http://www.chessex.com/Dice/Opaque%20Dice/25401.htm

My notes on angle and size estimates. All are based on a width of 10 units. Angle not shown is the angle of each face from the vertical ("leaning in"). The closest I got was 45.75 degrees from vertical.
http://home.ripway.com/2005-2/264571/LJ/d10_dimensions.jpg

Alas, all my nerdiness has amounted to nothing (for this endeavor). ;)
3rd-Apr-2005 03:49 pm (UTC)
Thanks for you help, I'll let you know if I get something that works.
3rd-Apr-2005 03:44 pm (UTC)
The d10 is a tricky shape. It's not a Platonic solid, of course. It's not even an Archimdian solid, because the sides are not regular polygons.

A "ten-sider" with perfectly flat sides has actually 20 sides, including ten small isoceles triangles around the equator, allowing the ten major sides to fit together. Since most people don't want the really sharp pointy ends, die manufacturers usually slice off the two "poles" and cap them with small regular pentagons.

For most modelling, this is irrelevant. The d10 virtually never lands on one of the end-cap pentagons, nor any of the little triangles. It has ten major bases, and it's symmetric, so that no base is larger, or more favored than any other. For modelling purposes, each face has a 0.1 chance of showing.
3rd-Apr-2005 03:48 pm (UTC)
I'm not trying to model the probability (which is easy), I'm trying to make a graphical model. So I need the coordinates of the points of each die in space, so that I can transform them and project them onto the screen. And knowing the proportions of each face would be helpful for this, because then I can figure out the angles in a plane and then extend that to space.
4th-Apr-2005 01:49 pm (UTC)
What program are you using to create the die? There might be an easier way than determining the coordinates of each vertex.

Lucifer >:}
4th-Apr-2005 02:14 pm (UTC)
I'm using the Graphics class in Java. I'm writing a program to creating the die, not using one :p