March 24, 2012 - Regular Icosahedron

If anyone is looking for a little weekend challenge:

Make a regular icosahedron (either as lines or a mesh).

Native Grasshopper components only, no scripts, no expressions.

and if that is too easy -

Try doing it with no referenced or typed inputs - so no text panels, internalized data, or manually set numbers.

How few components can you use?

Replies to This Discussion

Permalink Reply by Michael Pryor on March 24, 2012 at 11:49am

My attempt for now, I know there is a more effective way, plus my measurements vary slightly.

Attachments:

icosahedron attempt_pryor.gh, 6 KB

Permalink Reply by Mateusz Zwierzycki on March 24, 2012 at 12:06pm

here is mine, as correct and boring as possible :)

Attachments:

icosahedron.gh, 8 KB

Permalink Reply by Mateusz Zwierzycki on March 24, 2012 at 12:31pm

and now mesh icosahedron. I like the rounding part ;) Forgive me but faces are not welded(there are 20 singular meshes)... I didnt want to weld it because I dont remember now which mesh components are standard GH.

Attachments:

icosahedron.gh, 13 KB

Permalink Reply by Michael Pryor on March 24, 2012 at 12:35pm

nice one, I believe its the first definition I have seen to use golden ratio.

Permalink Reply by Luke Epp on March 24, 2012 at 1:28pm

My attempt at the second challenge - creating it with no referenced or typed inputs. Used a bit of maths to establish the ratios between the Icosahedral radius and the radius of the two inscribed Pentagons. The resulting Icosahedron is exact. Not a very elegant solution (and still needs an input of 5 for the number of sides of a pentagon!) but the closest I could get on a first attempt...

This Icosahedron is created using the radius of one of the internal Pentagons as a starting point.
Firstly, the ratio of the Icosahedral and Pentagonal radii must be:
Ricos / Rpent = Golden Ratio - 1/2

For a regular Icosahedron the two Pentagons must be parallel and separated by their Radius.

Thus the top and bottom vertices must be a distance of
Ricos - Rpent/2
from the two Pentagons. Using the above ratios however this simplifies to
Rpent x (Golden Ratio - 1).

Attachments:

IcosahedronLE.gh, 10 KB

Permalink Reply by Michael Pryor on March 24, 2012 at 3:11pm

Nice, but I think the point is not to explain it, or show the definition screenshot on here for people who still want to figure it out themselves, at least not until the deadline is up :) still great stuff.

Permalink Reply by Daniel Piker on March 24, 2012 at 5:59pm