Nesting Cubes, Recursive Cubes, Cubes within Cubes

Description

Nesting Cubes, Recursive Cubes, Cubes within Cubes This design is a 7-cube that has a 5-cube that has a 3-cube that has a unit cube. Each unit cube is 10 mm^3. Tolerance is added to allow the cubes to slide (nest) into each other. About the files Each cube has a bottom part and a top cover. The regular versions have a 0.4 mm clearance all around; the loose versions have a 0.5mm clearance. The top covers are the same as the clearance is added to the shells. The 3-cube top is the same as the unit cube. In addition to the recursive and geometric structures, there are a few questions to explore: How does the volume of a cube increase as we change the cube edge length from 1 unit, to 3, 5, and 7 units? What is the difference between the volume of the 7-cube and that of the 5-cube? How does one count the number of unit cubes if we take a 5-cube core out of a 7-cube? If one counts 7^2 cube on each face and multiply that by six, how should the number be adjusted to find the actual number of unit cubes? Hints: Each vertex is counted three times; each edge is counted two times. Pose your own questions. References Cubic numbers. http://mathworld.wolfram.com/CubicNumber.html https://en.wikipedia.org/wiki/Recursion https://en.wikipedia.org/wiki/Matryoshka_doll