Nesting Cubes, Recursive Cubes, Cubes within Cubes

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Nesting Cubes, Recursive Cubes, Cubes within Cubes This design features a 7-cube made up of a 5-cube made up of a 3-cube made up of a unit cube. Each unit cube measures 10 mm^3 in volume. To allow the cubes to fit together smoothly, a tolerance is added. About the Files 1. Each cube consists of two parts: a bottom part and a top cover. 2. Regular versions have a 0.4 mm clearance around them, while loose versions have a 0.5mm clearance. 3. The top covers are identical to the cubes, as the clearance is added to their shells. In addition to exploring recursive and geometric structures, several questions can be asked: 1. How does the volume of a cube change when its edge length increases from 1 unit to 3, 5, and 7 units? 2. What is the difference in volume between the 7-cube and the 5-cube? 3. If we remove a 5-cube core from a 7-cube, how many unit cubes are there? To calculate this, we can start by counting 7^2 cube on each face and multiply that number by six. However, since each vertex is counted three times and each edge is counted twice, the actual number of unit cubes needs to be adjusted accordingly. References 1. Cubic numbers: http://mathworld.wolfram.com/CubicNumber.html 2. Recursion: https://en.wikipedia.org/wiki/Recursion 3. Matryoshka doll: https://en.wikipedia.org/wiki/Matryoshka_doll