Dodecahedron  Printable Version + LDraw.org Discussion Forums (https://forums.ldraw.org) + Forum: General (https://forums.ldraw.org/forum12.html) + Forum: General LDraw.org Discussion (https://forums.ldraw.org/forum6.html) + Thread: Dodecahedron (/thread23457.html) Pages:
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Dodecahedron  Philippe Hurbain  20190604 After seeing this in LEGO House: https://photos.app.goo.gl/bAAXaEebvrTMJfZZ6... I feeled urged to create a LDraw model! I was too lazy to create a flexed axle template for LDCad so I used 12L rigid tubing instead, but it does the job! RE: Dodecaedron  Roland Melkert  20190604 (20190604, 18:03)Philippe Hurbain Wrote: After seeing this in LEGO House: https://photos.app.goo.gl/bAAXaEebvrTMJfZZ6... I feeled urged to create a LDraw model! Very cool, how did you get the positions of those axle joiners? RE: Dodecaedron  Steffen  20190604 awesome. I also wonder like Roland how you found the positions of the connectors in advance RE: Dodecahedron  Philippe Hurbain  20190605 (20190604, 22:29)Steffen Wrote: awesome.Problem is not so much to get connector positions (dodecahedron vertices coordinates are known: https://en.wikipedia.org/wiki/Regular_dodecahedron#Cartesian_coordinates), 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_dodecahedron#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°) ) [attachment=3719] 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... RE: Dodecahedron  Jaco van der Molen  20190605 (20190605, 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_dodecahedron#Cartesian_coordinates), but to have them in the right orientation. Don't we all just LOVE maths? Truncated icosahedron  Philippe Hurbain  20190606 Using a similar method (a bit complicated because all edges are not equivalent) I also made a truncated icosahedron (soccer balls, geodesic domes, fullerenes, etc...). Enjoy! [attachment=3724] RE: Dodecahedron  Steffen  20190606 I love this. Lego should make a set with the 5 platonic solids https://en.wikipedia.org/wiki/Platonic_solid RE: Dodecahedron  Magnus Forsberg  20190606 Witchcraft. I love it. If I remember correct, Isn't there a way to inscribe all the Platonic solids into one another? There is a cube inside the dodecahedron, and there's a octahedron inside the cube, and so on... RE: Dodecahedron  Orion Pobursky  20190606 (20190606, 21:24)Magnus Forsberg Wrote: Witchcraft. I love it. Yah. Stellate the corner point of the faces out to a center point and then connect those points. Pyramid > Pyramid Cube > Octohedron Dodecahedron > Icosahedron. RE: Dodecahedron  Philippe Hurbain  20190607 (20190606, 21:41)Orion Pobursky Wrote: Yah. Stellate the corner point of the faces out to a center point and then connect those points.I think Magnus rather meant something like this: https://www.youtube.com/watch?v=gwxQfujwWrw 