Interlocking Puzzle Cube

This project is aimed at students and educators in mathematics classes, as well as individuals interested in 3D design and printing. The focus is on applying mathematical concepts such as geometry, symmetry, and spatial reasoning to design a cube divided into two or more interlocking, puzzle-like parts. An example of the kind of geometric exploration used in this project can be found in this GeoGebra model, which demonstrates the power of 3D geometry. This project is ideal for high school or middle school students in STEAM or mathematics programs, as it combines practical 3D design with theoretical mathematics, providing a hands-on approach to understanding abstract concepts.

Participants should have a basic understanding of mathematics, particularly geometry, including concepts like shapes, dimensions, symmetry, and transformations (e.g., rotations, reflections). Familiarity with CAD software is helpful but not required, as step-by-step instructions are provided. Basic knowledge of 3D printing processes, including slicing and printer operation, is useful but can also be learned during the project. An interest in creative problem-solving and spatial thinking is essential.

The main objective is to design and create a 3D-printable cube divided into two or more interlocking puzzle-like parts. The project emphasizes the application of mathematical concepts, such as calculating dimensions, analyzing symmetry, and understanding spatial relationships. By combining these principles with CAD modeling and 3D printing, participants gain practical experience in problem-solving and technical skills while reinforcing their understanding of mathematics.

• 3D Printer: A standard printer for PLA or similar materials.
• CAD Software: Tools like Tinkercad, GeoGebra, or Fusion 360 to design puzzle-like connections.
• Slicing Software: For preparing STL files for printing (e.g., PrusaSlicer).
• 3D Printing Materials: PLA or another filament.
• Computer: With necessary CAD and slicing software installed.
• Measurement Tools: For testing tolerances and ensuring accurate part fitting.

The project can be completed within the following timeline:

Day 1 – Introduction (1-2 hours):

• Overview of the project, objectives, and required mathematical concepts.
• Introduction to CAD software and its basic tools.

Day 2 – Design Phase (2-3 hours):

• Brainstorming puzzle-like splitting designs.
• Modeling the cube with interlocking connections in CAD software.

Day 3 – Printing Phase (2-4 hours):

• Exporting the design to STL and slicing it for printing.
• Printing the parts and troubleshooting any potential issues.

Day 4 – Assembly and Evaluation (1-2 hours):

• Assembling and testing the printed parts for proper fit.
• Discussing improvements and evaluating the mathematical and design process.

Planning and Preparation:

• Participants learn about the mathematical principles involved, such as symmetry and transformations.
• Brainstorm creative puzzle-like designs for splitting the cube into two or more parts.

Designing the Cube:

• Use CAD software to create a cube and split it into interlocking puzzle-like parts.
• Apply geometry and symmetry principles to ensure parts fit perfectly.

Preparing for Printing:

• Export the completed model as an STL file and slice it using slicing software.
• Adjust tolerances and settings to optimize for 3D printing.

3D Printing the Parts:

• Print the interlocking parts and monitor the process to ensure quality.

Testing and Assembly:

• Assemble the printed parts and test their fit. If necessary, identify and address any fitting issues.

Reflection and Discussion:

• Reflect on the mathematical concepts applied, the design process, and potential improvements.
• Discuss the connection between theoretical mathematics and practical applications.