Dodecahedron

RE: Dodecahedron
#5
(2019-06-05, 7:01)Philippe Hurbain Wrote: Problem is not so much to get connector positions (dodecahedron vertices coordinates are known: https://en.wikipedia.org/wiki/Regular_do...oordinates), but to have them in the right orientation.
Here is the method I used:
- Get the distance between connectors. I used a visual method for that, placing two connectors with roughly the right orientation, then changing the distance until I got the desired length (96mm = 12L) for the flex part I put between them. Turns out the distance is 252 LDU.
- Calculate the radius r of the circumscribed sphere[url=https://en.wikipedia.org/wiki/Circumscribed_sphere][/url] (https://en.wikipedia.org/wiki/Regular_do...Dimensions): 353.117LDU.
- Because of symmetry, a connector must be tangent to this sphere. So I placed a connector at y=-353.117, above the middle of top face.
- Then calculate the angle I must turn that connector around origin to place it on one top pentagon vertex. We get alpha = arcsin(r1/r)=37.377° (r1 is radius of circumscribed circle of pentagon with side a = a/2/sin(36°) )

After that, it's only a matter of duplication, rotation by 72° around world Y axis and rotation by 120° around of Y local axis of already placed connectors...

Don't we all just LOVE maths?
Jaco van der Molen
lpub.binarybricks.nl
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 Messages In This Thread Dodecahedron - by Philippe Hurbain - 2019-06-04, 18:03 RE: Dodecaedron - by Roland Melkert - 2019-06-04, 19:04 RE: Dodecaedron - by Steffen - 2019-06-04, 22:29 RE: Dodecahedron - by Philippe Hurbain - 2019-06-05, 7:01 RE: Dodecahedron - by Jaco van der Molen - 2019-06-05, 11:18 RE: Dodecahedron - by Steffen - 2019-06-06, 21:11 RE: Dodecahedron - by Magnus Forsberg - 2019-06-06, 21:24 RE: Dodecahedron - by Orion Pobursky - 2019-06-06, 21:41 RE: Dodecahedron - by Philippe Hurbain - 2019-06-07, 7:48 RE: Dodecahedron - by Magnus Forsberg - 2019-06-07, 8:21 RE: Dodecahedron - by Steffen - 2019-06-08, 20:33 Truncated icosahedron - by Philippe Hurbain - 2019-06-06, 8:20

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