https://github.com/qalle2/plato

Platonic solids for OpenSCAD
https://github.com/qalle2/plato

3d-geometry geometry openscad

Last synced: 5 months ago
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Platonic solids for OpenSCAD

• Host: GitHub
• URL: https://github.com/qalle2/plato
• Owner: qalle2
• License: gpl-3.0
• Created: 2018-08-10T13:24:44.000Z (almost 8 years ago)
• Default Branch: main
• Last Pushed: 2021-02-10T20:35:37.000Z (over 5 years ago)
• Last Synced: 2025-03-08T06:42:10.583Z (over 1 year ago)
• Topics: 3d-geometry, geometry, openscad
• Language: OpenSCAD
• Homepage:
• Size: 23.4 KB
• Stars: 5
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

          
# plato

*Note: This project has been moved to [Codeberg](https://codeberg.org/qalle/openscad-solids). This version will no longer be updated.*

The non-built-in Platonic solids for OpenSCAD:

* regular tetrahedron (four faces)

* regular octahedron (eight faces)

* regular dodecahedron (12 faces)

* regular icosahedron (20 faces)

## Screenshot

![screenshot](plato.png)

## References

Wikipedia:

* [Platonic solid](https://en.wikipedia.org/wiki/Platonic_solid)

* [equilateral triangle](https://en.wikipedia.org/wiki/Equilateral_triangle)

* [regular tetrahedron](https://en.wikipedia.org/wiki/Tetrahedron#Regular_tetrahedron)

* [regular octahedron](https://en.wikipedia.org/wiki/Octahedron#Regular_octahedron)

* [regular dodecahedron](https://en.wikipedia.org/wiki/Regular_dodecahedron)

* [regular icosahedron](https://en.wikipedia.org/wiki/Regular_icosahedron)

## Math

*a* denotes the edges of all the solids.

phi:

* *ϕ* = (1 + √5) / 2

* *ϕ*² = *ϕ* + 1

### Regular tetrahedron

* incircle (faces): *r* = √(3) / 6 × *a*

* circumcircle (faces): *R* = √(3) / 3 × *a*

* insphere: *r* = √(6) / 12 × *a*

* circumsphere: *R* = √(6) / 4 × *a*

### Regular octahedron

* circumsphere: *R* = √(2) / 2 × *a*

### Regular dodecahedron

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)

### Regular icosahedron

Coordinates of vertices if *a* = 1:

* circular permutations of (0, ±½, ±*ϕ*/2)