LDraw.org Discussion Forums
Dodecahedron - Printable Version

+- LDraw.org Discussion Forums (https://forums.ldraw.org)
+-- Forum: General (https://forums.ldraw.org/forum-12.html)
+--- Forum: General LDraw.org Discussion (https://forums.ldraw.org/forum-6.html)
+--- Thread: Dodecahedron (/thread-23457.html)

Pages: 1 2


Dodecahedron - Philippe Hurbain - 2019-06-04

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 - 2019-06-04

(2019-06-04, 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!

I was too lazy to create a flexed axle template for LDCad so I used 12L rigid tubing instead, but it does the job!

Very cool, how did you get the positions of those axle joiners?


RE: Dodecaedron - Steffen - 2019-06-04

awesome.
I also wonder like Roland how you found the positions of the connectors in advance


RE: Dodecahedron - Philippe Hurbain - 2019-06-05

(2019-06-04, 22:29)Steffen Wrote: awesome.
I also wonder like Roland how you found the positions of the connectors in advance
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 - 2019-06-05

(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_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°) )


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?  Big Grin


Truncated icosahedron - Philippe Hurbain - 2019-06-06

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 - 2019-06-06

I love this.

Lego should make a set with the 5 platonic solids
https://en.wikipedia.org/wiki/Platonic_solid


RE: Dodecahedron - Magnus Forsberg - 2019-06-06

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 - 2019-06-06

(2019-06-06, 21:24)Magnus Forsberg Wrote: 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...

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 - 2019-06-07

(2019-06-06, 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