Grasshopper

algorithmic modeling for Rhino

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?

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

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

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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. 

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

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).

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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. 

Great to see the range of ways this is possible.

How about with less than 10 components ?...

slider is counted ?

7 components, no typed data or sliders ... but there is a line missing

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impressive!

just for closure 10 components and all lines are present and correct.

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Here's the shortest I could come up with

a few more possible solutions here:

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