Polyhedron (beta)

Background

The first one was to find some enjoying math material on the net for the kids. I found the great Virtual Polyhedra page by George Hart. George provides 789 data files free for noncommercial purposes. However, these are in the VRML format which seems to become less and less supperted.

The second activity consists in trying to understand HTML5+Javascript+WebGL. Though I have not much time to invest into such stuff, I am interested in it as it seems to become a great possibility to do widely portable interactive stuff. I come from a background of numerical algorithm development, so coding and OpenGL visualization is familiar for me.

The convergence of these activities resulted in this page (which still is in beta stage and might stay so for a while). I did the following steps to create it:

• Took the VRML files from the Virtual Polyhedra page, extracted point+face data and stored the resulting information in JSON format using this Lua script into this directory . So far, there was no time to check the consistency of all these models.
• Cloned the Hello World example of the Three.js framework started by Ricardo Cabello aka mrdoob into a quick-and-dirty viewer for the converted polyhedron files.

Polyhedra

• The Five Platonic Solids
  • tetrahedron
  • cube
  • octahedron
  • dodecahedron
  • icosahedron
• The Kepler-Poinsot Polyhedra
  • great stellated dodecahedron, {5/2, 3}
  • small stellated dodecahedron, {5/2, 5}
  • great icosahedron
  • great dodecahedron
• 59 Stellations of the Icosahedron

  See also the correspondig page by George Hart. So far I was not able to extract his color scheme.

  • 1. A (icosahedron), [4] (solid color) (5 colors)
  • 2. B (first stellation), [26] (solid color) (5 colors)
  • 3. C (five octahedra), [23] (solid color) (5 colors)
  • 4. D (solid color) (5 colors)
  • 5. E (solid color) (5 colors)
  • 6. F, [27] (solid color) (5 colors)
  • 7. G (great icosahedron), [41] (solid color) (5 colors)
  • 8. H (final stellation), [42] (solid color) (5 colors)
  • 9. e1, [37] (solid color) (5 colors)
  • 10. f1 (solid color) (5 colors)
  • 11. g1, [29] (solid color) (5 colors)
  • 12. e1f1 (solid color) (5 colors)
  • 13. e1f1g1 (solid color) (5 colors)
  • 14. f1g1 (solid color) (5 colors)
  • 15. e2 (solid color) (5 colors)
  • 16. f2 (the only disconnected one) (solid color) (5 colors)
  • 17. g2 (solid color) (5 colors)
  • 18. e2f2 (solid color) (5 colors)
  • 19. e2f2g2 (solid color) (5 colors)
  • 20. f2g2, [30] (solid color) (5 colors)
  • 21. De1, [32] (solid color) (5 colors)
  • 22. Ef1 (ten tetrahedra), [25] (solid color) (5 colors)
  • 23. Fg1, [31] (solid color) (5 colors)
  • 24. De1f1 (solid color) (5 colors)
  • 25. De1f1g1 (solid color) (5 colors)
  • 26. Ef1g1, [28] (solid color) (5 colors)
  • 27. De2 (solid color) (5 colors)
  • 28. Ef2 (solid color) (5 colors)
  • 29. Fg2, [33] (solid color) (5 colors)
  • 30. De2f2, [34] (solid color) (5 colors)
  • 31. De2f2g2 (solid color) (5 colors)
  • 32. Ef2g2 (solid color) (5 colors)
  • 33. f1, [35] (solid color) (5 colors)
  • 34. e1f1, [36] (solid color) (5 colors)
  • 35. De1f1 (solid color) (5 colors)
  • 36. f1g1 (solid color) (5 colors)
  • 37. e1f1g1, [39] (solid color) (5 colors)
  • 38. De1f1g1 (solid color) (5 colors)
  • 39. f1g2 (solid color) (5 colors)
  • 40. e1f1g2 (solid color) (5 colors)
  • 41. De1f1g2 (solid color) (5 colors)
  • 42. f1f2g2 (solid color) (5 colors)
  • 43. e1f1f2g2 (solid color) (5 colors)
  • 44. De1f1f2g2 (solid color) (5 colors)
  • 45. e2f1, [40] (solid color) (5 colors)
  • 46. De2f1 (solid color) (5 colors)
  • 47. Ef1 (five tetrahedra), [24] (solid color) (5 colors) (anti-colored)
  • 48. e2f1g1 (solid color) (5 colors)
  • 49. De2f1g1 (solid color) (5 colors)
  • 50. Ef1g1 (solid color) (5 colors)
  • 51. e2f1f2, [38] (solid color) (5 colors)
  • 52. De2f1f2 (solid color) (5 colors)
  • 53. Ef1f2 (solid color) (5 colors) (anti-colored)
  • 54. e2f1f2g1 (solid color) (5 colors)
  • 55. De2f1f2g1 (solid color) (5 colors)
  • 56. Ef1f2g1 (solid color) (5 colors)
  • 57. e2f1f2g2 (solid color) (5 colors)
  • 58. De2f1f2g2 (solid color) (5 colors)
  • 59. Ef1f2g2 (solid color) (5 colors)
• Clone of the alphabetic list by George Hart. Please note that some models might be broken. If so, this would be entirely my fault, not George's.

(c) 2013 Jürgen Fuhrmann, juergen-fuhrmann@web.de
With extensive use of material from Virtual Polyhedra, (c) George W. Hart