Story behind the project......
The polypod project was originated from a real-life engineering project almost 50 years ago. At that time, my dad was tackling an open challenge to build tetrapods for his company. Tetrapods are huge four-leg symmetrical concrete structure which are used to protect the seashore. (Tetrapods photos in Japan)
My dad used his high-school math training in geometry and trigonometry to solve the problem and build the tetrapods. After that project, due to his curiosity, he continued to research the topic and developed a series of polypods based on regular (also called Platonic Solid) and some semi-regular polyhedrons (also called Archimedean Solid).
Historical PolypodThe photo shows that I held a 32-tube polypod as my gift toy from my dad when I was very young. The polypod is based on the 32-face Icosidodecahedron. An icosidodecahedron is a polyhedron with twenty triangular faces and twelve pentagonal faces. (More information of Icosidodecahedron)
Polypod Photo Gallery
Here are some polypods examples which I built for the precalculus project in 2008.
- two tubes joint together with 45-degree cuts and form an I shape
- three tubes joint together with 45-degree cuts and form a Z shape
- Three tubes joint together with 120 degree between each pair of tubes
- Two tubes joint together to form T shape with 90 degree between them
- Based on the Tetrahedron
- A mutated version of Tetrapod with the top three tubes sitting on the same plane like a Tripod
- Based on the Hexahedron (Cube)
- Based on the Octahedron
- Based on the Dodecahedron
- Based on the Isocahedron
Student Polypod Project Photo Gallery (Precal 2008)
How to Build a Polypod?
The tetrapod will be used as an example to illustrate the steps of building a polypod.
[1] Calculate the "central angle" between any pair of the tubes. This angle is the supplementary angle of the "dihedral angle" of tetrapod. The dihedral angle and central angle can be calculated using basic geometry and trigonometry. (Example of central and dihedral angles calculation). The dihedral angle of tetrapod is 70.52877936 degrees, and the central angle is 109.47122064 degrees.
[2] Use planar unfolding skills to draft the unfolded diagram of the tube which will be cut at half of the central angle. An example of the unfolding diagram is shown in the following.
[3] Clean up the draft, copy & paste, and create a template for the Tetrapod. Cut and glue each tube, and then, tape them together to form a beautiful Tetrapod. Don't forget to leave some extra space for gluing. An example template of the Tetrapod is shown in the following.
The same steps can be used to build the polypods based on different polyhedrons.
