Nesting Cubes, Recursive Cubes, Cubes within Cubes

cults3d

Nesting Cubes, Recursive Cubes, Cubes within Cubes This design is a 7-cube that contains a 5-cube which in turn holds a 3-cube and finally includes a unit cube. Each single unit cube measures 10 mm^3. To allow the cubes to slide into each other, tolerance is added. About the Files 1. Each cube has two parts: a bottom section and a top cover. 2. Regular versions have a 0.4 mm clearance all around, while loose versions have a 0.5mm clearance. 3. The top covers are identical since the clearance is added to the shells. The 3-cube top is equivalent to the unit cube. In addition to the recursive and geometric structures, several questions can be explored: How does the volume of a cube change as we alter the cube edge length from 1 unit to 3 units, then to 5 units, and finally to 7 units? What is the difference between the volume of the 7-cube and that of the 5-cube? To count the number of single unit cubes when removing a 5-cube core from a 7-cube, one can start by calculating 7^2 for each face and then multiply this number by six. However, to find the actual number of unit cubes, adjustments must be made. Hints: Each vertex is counted three times; each edge is counted two times. Pose your own questions. References 1. Cubic numbers. http://mathworld.wolfram.com/CubicNumber.html 2. https://en.wikipedia.org/wiki/Recursion 3. https://en.wikipedia.org/wiki/Matryoshka_doll