number of bodies in cubic space

[shahar]

If I limited a body in a space figure that is a cube.
How many polyhedral bodies can be legal body (I meant closed, with integer size of faces and edges) in a given space of cube?
There is a way to calculate it?!
I give example of plane:
In 2 x 2 plane that a body I can put 1 square, a 2 x 1 triangle.

There is link dealing with this problem? If there add it, please.

 

[JeffM]

I do not understand what you are asking.

In a square with sides of length 2, you can place four congruent squares, each with sides of length 1, and you can place eight congruent equilateral triangles, each with sides of lenth 1. There is no unused space in the case of the four square. Percentage of available space not used in the case of the triangles is

[MATH]100 * \dfrac{4 - \left ( 8 * \dfrac{1}{2} * 1 * \dfrac{\sqrt{3}}{2} \right )}{4} = 100 \left (1 - \dfrac{\sqrt{3}}{2} \right ) \approx 13.4\%.[/MATH]
I'd start by looking up packing problems.