Icosahedron by Code
I tried different approaches to drawing platonic solids using Grasshopper’s native components. However, it seems impossible now. In geometric definition, a platonic solid is a set of points, distributed on a sphere with equal distances. If the set contains 12 points, then it’s an icosahedron. I found lots of information about these objects and mathematicians seem to love analyzing them. They created different approaches to building an icosahedron. One of them is very suitable to implement on Grasshopper’s VB component. They defined the exact relative coordinates of each point. This was a good experiment for me to remember the good old days of coding. I didn’t prefer using codes to define algorithms for almost three years. Maybe there are still very good reasons to return to it.
Dim pi, R, H1, H2, Z1, Z2, H, Cx, Cy As Double
Dim po(11) As Point3d
Dim ed(31) As line
pi = 4 * System.Math.atan(1)
R = (S / 2) / System.Math.Sin(pi / 5)
H = System.Math.Cos(pi / 5) * R
H1 = System.Math.Sqrt(S * S - R * R)
H2 = System.Math.Sqrt((H + R) * (H + R) - H * H)
Z2 = (H2 - H1) / 2
Z1 = Z2 + H1
Cx = R * System.Math.Cos(pi / 10)
Cy = R * System.Math.Sin(pi / 10)
po(0) = New Point3d(0, 0, Z1)
po(1) = New Point3d(0, R, Z2)
po(2) = New point3d(Cx, Cy, Z2)
po(3) = New point3d(S / 2, -H, Z2)
po(4) = New point3d(-S / 2, -H, Z2)
po(5) = New point3d(-Cx, Cy, Z2)
po(6) = New point3d(0, -R, -Z2)
po(7) = New point3d(-Cx, -Cy, -Z2)
po(8) = New point3d(-S / 2, H, -Z2)
po(9) = New point3d(S / 2, H, -Z2)
po(10) = New point3d(Cx, -Cy, -Z2)
po(11) = New point3d(0, 0, -Z1)
V = poCite this post
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