# Nesting Cubes, Recursive Cubes, Cubes within Cubes

## 3D model 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.

1. Each cube has a bottom part and a top cover.
2. The regular versions have a 0.4 mm clearance all around; the loose versions have a 0.5mm clearance.
3. 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:

1. How does the volume of a cube increase as we change the cube edge length from 1 unit, to 3, 5, and 7 units?
2. What is the difference between the volume of the 7-cube and that of the 5-cube?
3. 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.

### #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

• 3D model format: STL

## Creator

STEAM educator, learning from and working with K-12 STEAM teachers to explore new ideas of teaching and engagement. I firmly believe ART is at the core of STEM learning or all human learning! I owe my ideas and designs to the hundreds of K-12 children and teachers and university professors I have had the pleasure of working with, in multiple disciplines-- math, science,engineering language arts, social studies, early childhood education and more! All mistakes, of course, are mine! There is no warranty or liability whatsoever implied or explicit behind the designs or ideas. They are all posted for their potential educational values.

When working with children, please strictly observe all safety and health procedures! Please refer to the NSTA safety guides: http://www.nsta.org/safety/.

LGBU Contact: LGBU@SIU.EDU