The non-built-in Platonic solids for OpenSCAD:
- regular tetrahedron (four faces)
- regular octahedron (eight faces)
- regular dodecahedron (12 faces)
- regular icosahedron (20 faces)
Wikipedia:
- Platonic solid
- equilateral triangle
- regular tetrahedron
- regular octahedron
- regular dodecahedron
- regular icosahedron
a denotes the edges of all the solids.
phi:
- ϕ = (1 + √5) / 2
- ϕ² = ϕ + 1
- incircle (faces): r = √(3) / 6 × a
- circumcircle (faces): R = √(3) / 3 × a
- insphere: r = √(6) / 12 × a
- circumsphere: R = √(6) / 4 × a
- circumsphere: R = √(2) / 2 × a
If a = 2/ϕ, the coordinates of the vertices are:
- (±1, ±1, ±1)
- circular permutations of (0, ±ϕ, ±1/ϕ)
To get coordinates for a = 1, multiply them by ϕ/2:
- (±ϕ/2, ±ϕ/2, ±ϕ/2)
- circular permutations of (0, ±(ϕ+1)/2, ±½)
Coordinates of vertices if a = 1:
- circular permutations of (0, ±½, ±ϕ/2)