1. Chin-Sung Lin Eleanor Roosevelt High School

2. In the Beginning …… The polypod project was originated from a real-world engineering project more than 50 years ago.

3. In the Beginning …… At that time, a young, high school graduate was tackling an open challenge in his company to build tetrapods.

4. In the Beginning …… Tetrapods are huge four-leg symmetrical concrete structures that are used to protect the seashore from erosion.

5. In the Beginning …… A tetrapod's shape is designed to dissipate the force of incoming waves, and to reduce displacement by allowing a random distribution of tetrapods to mutually interlock.

6. In the Beginning …… This young engineer used his high-school math training in geometry and trigonometry to solve the problem.

7. In the Beginning …… He successfully built lots of tetrapods for his company!

8. In the Beginning …… After that project, due to his curiosity, he continued to research the topic and developed a series of polypods.

9. In the Beginning …… He later made an Icosidodecapod for his son as a gift,…… and his son made this presentation.

10. Regular Polyhedrons Polypods are based on regular polyhedrons (also called Platonic Solid)

11. Semi-Regular Polyhedrons Polypods are also based on semi-regular polyhedrons (also called Archimedean Solid).

12. Polypods and Polyhedrons The Tetrapod is based on the Tetrahedron.

13. Polypods and Polyhedrons The Hexapod is based on the Hexahedron.

14. Polypods and Polyhedrons The Octapod is based on the Octahedron.

15. Polypods and Polyhedrons The Dodecapod is based on the Dodecahedron.

16. Polypods and Polyhedrons The Icosapod is based on the Icosahedron.

17. Polypods and Polyhedrons The Icosidodecapod is based on the Icosidodecahedron.

18. Dihedral Angles and Central Angles A Dihedral Angle of a polyhedron is the angle between two neighboring faces. φ φ

19. Dihedral Angles and Central Angles A Dihedral Angle (φ) is always supplementary to the Central Angle (ϑ). φ ϑ

20. φ Dihedral Angles and Central Angles A Dihedral Angle (φ) is always supplementary to the Central Angle (ϑ). ϑ

21. ϑ Dihedral Angles and Central Angles A Central Angle (ϑ) is the angle between two neighboring tubes of a polypod. ϑ

22. ϑ Dihedral Angles and Central Angles The cut angle (ϑ/2) of the tubes of a polypod is equal to half of its Central Angle. ϑ/2

23. Dihedral Angles and Central Angles We need to calculate the corresponding cut angle of the tubes in order to build a specific polypod. The cut angle is the complementary angle of ϑ/2. Cut angle = 90 o – ϑ/2 = φ/2. ϑ/2 φ/2

24. 2D Drawings of 3D Tubes Polypods are made of different number of tubes. PolypodPolyhedronNo. of Tubes TetrapodTetrahedron4 HexapodHexahedron6 OctapodOctahedron8 DodecapodDodecahedron12 IcosapodIcosahedron20

25. 2D Drawings of 3D Tubes (Hexapod) The 3D tubes can be drew in 2D based on different views. Top View Side View

26. 2D Drawings of 3D Tubes (Hexapod) 1.Define and draw the top view, side view, and unfolding view. Top View Side View Unfolding View Circumference Diameter Length

27. 2D Drawings of 3D Tubes (Hexapod) 2.Draw a cut on the circle, and indicate the cut angle on the side view. Cut -The number of cuts (n) in the circle is equal to the number of neighboring tubes (n). - The number of cuts (n) determines the angle of the section (α), where α = 2π / n. - The cut should be symmetric to the horizontal line passing through the center of circle. α Cut Angle - The cut angle is determined by the type of polypod. - The cut angle is equal to half of the Dihedral angle (φ). ϑ/2 φ/2

28. 2D Drawings of 3D Tubes (Hexapod) 3.Divide the cut into divisions, and show them on the unfolding view. Divisions -The number of divisions in a section (d) is determined by the designer. -Only needs to show the upper half of the section. Divisions -The number of divisions on the circumference is equal to n  d

29. 2D Drawings of 3D Tubes (Hexapod) 4.Project divisions onto the side view and show the real cut accordingly. Projected Divisions -The locations of the divisions have been projected vertically onto the side view. Side View of the Cut -The cut will follow the cut angle.

30. 2D Drawings of 3D Tubes (Hexapod) 5.Project the intercepts horizontally onto the unfolding view. Projected Divisions -The locations of the divisions have been projected horizontally onto the unfolding view.

31. 2D Drawings of 3D Tubes (Hexapod) 6.Connect intercepts with smooth curves (interpolation splines). Connect Intercepts to form Curves -The corresponding intercepts will be connected with smooth curves. -These curves are the real 2D cuts of -3D tubes.

32. 2D Drawings of 3D Tubes (Hexapod) 7.Clean up the drawing and create a template for polypod tubes. Template of Tube -Trim and delete redundant drawings to revel the tube template. -Don’t forget to keep a copy of the complete drawing before cleaning up.

33. 2D Drawings of 3D Tubes (Hexapod) 8.Duplicate the template and print it out. Copies of Template -Make n copies of template

34. Polypod Construction

35. The World of Polypods

36. Q & A