Profile image

Regular Icosahedron

46.6k SnoWFLakE0s  one month ago

An icosahedron is a polyhedron with 20 faces. In particular, this is the regular, convex, non-stellated icosahedron, which is one of the Platonic solids, and is composed of 20 equilateral triangles. Link to Wikipedia article here.

The model provided uses equilateral triangles with a side length of 1 fuselage unit.

This model was constructed by hand using some math.

  1. The top "pentagon" was constructed by calculating the apothem of the orthographic projection of the pentagon, using that as a leg for a theoretical triangle between the pentagon projection and an inclined triangle, leading to the angle 37.38º. Link to math here.
  2. I used two of the previous "pentagon" bits with one on top and one on the bottom. Now I had to fill in the sides, which meant I had to calculate the inclination angle for the side triangle panels. I again constructed a theoretical triangle between the top pentagon and bottom pentagon. There was a horizontal difference which came down to the difference of the pentagon's circumradius and apothem, which gave me an angle of 10.81º from the normal for the side triangles.
  3. I had to also figure out the block positions, which took most of my time actually. It was mostly figuring out the position of the vertices and using those to calculate the position for other bits. Link to math here.

TL;DR: annoying trigonometry to figure out block positions.

I was originally trying to create buckminsterfullerene but this looked easier to start with so I took around an hour and a half to build this. It looks nice, sort of like one of those "power crystal" things in games.

Hope this is somehow useful, have fun!
- Snow


General Characteristics

  • Successors 1 airplane(s) +21 bonus
  • Created On Mac
  • Wingspan 2.7ft (0.8m)
  • Length 2.8ft (0.9m)
  • Height 3.1ft (1.0m)
  • Empty Weight 551lbs (250kg)
  • Loaded Weight 551lbs (250kg)


  • Wing Loading -439,839.3lbs/ft2 (-2,147,483.6kg/m2)
  • Wing Area 0.0ft2 (0.0m2)
  • Drag Points 51


  • Number of Parts 1
  • Control Surfaces 0