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Modelo 3D Improved Polydron panels por Kladrie no Thingiverse

Descrição

The original Polydron panels consisted of triangles, squares, pentagons, and hexagons, all with identical side lengths, which cleverly interlock to enable construction of various 3-dimensional shapes. (See e.g. https://www.polydron.co.uk/construction/polydron-class-set.html). I had much joy with mine.

See also the compatible Polydron Frameworks version, for your printing pleasure.

Based on years of use, a number of drawbacks to the original Polydron panels were identified:

  1. Cost and availability, being high and low respectively. The rate of exchange of the British pound does not help and neither does residing in the colonies.
  2. Durability - over the years I have had to retire quite a few of my precious panels, mainly due to cracks in the plastic finger acting as a spring to allow the interlocking mechanism to engage, and to stay engaged.
  3. Tightness of fit - perhaps related to the previous problem, not all edge joins are sufficiently tight/robust to withstand even gentle handling.
  4. Minimum angle between panels – this is limited to about 55°, at which point the interlocking mechanism starts taking strain, and is on the verge of disengaging.
  5. Rhombi: long ago Polydron also made two types of rhombus, with the ratio between the long and short axes being sqrt(2) and the golden ratio (1.4142 and 1.618) respectively. This enables the construction of, amongst others, rhombic dodecahedra and rhombic triacontahedra, and is in general just cool. However, probably because the unwashed masses did not appreciate said coolness (as is their wont, most depressingly), these pieces seem to have been discontinued, and by the time I had the money to possibly afford it, it was too late. Tears were shed.

So, while rectifying the final issue listed above, seemingly all the others were also inadvertently addressed. Increasing the relevant edge clearance has reduced the minimum angle between panels to about 40°, and the fit has been made slightly tighter on purpose. Only time will tell if the durability issue has been truly solved, but of course it is now a simple matter to run off another batch if things do wear out.

You can never have enough triangles; after much experimentation I was able to fit 18 on the 250x210mm bed of my Prusa Mk4 - see file Triangle x18.3mf.

An interesting article on the desirability of rhombi: https://archive.bridgesmathart.org/2013/bridges2013-71.pdf

Of the rhombi you want at least a dozen of the Sqrt(2) version, to make a rhombic dodecahedron, and probably lots more after reading the article referenced above. And you need no fewer than 30 of the golden ratio rhombi (denoted by the Greek letter phi φ) for a triacontahedron, after which the rhombic hexecontahedron with its 60 golden ratio faces is an almost irresistible goal.

Thingiverse

Improved Polydron panels

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construction educational Educational Toy geometry geometry toys Polydron stem
Licença Creative Commons - Attribution - Non-Commercial - Share Alike
Arquivos (8)
RhombSqrt2.stl 370.8 KB
RhombPhi.stl 385.5 KB
Triangle.stl 2.9 MB
Square.stl 3.7 MB
Pentagon.stl 4.5 MB
Hexagon_solid.stl 5.3 MB
Hexagon_trihole.stl 8.6 MB
Hexagon_frame.stl 6.2 MB
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