/spec sheet · polyhedra.py
Spec sheet · polyhedra.py

polyhedra.py

The five Platonic solids as watertight polyhedra — sized by circumradius, diameter, inradius or side. The dodecahedron is built as the dual of the icosahedron.

tetrahedron(r=15)interactive · drag to orbit
icosahedron · 12 v · 30 e · 20 f

rendered & measured

watertight

Vertices come from exact φ-based coordinates, normalised to a unit circumradius and scaled to the requested size. Every one closes watertight, winding included.

variants · click to load
4triangles
1,732.1mm³ volume
17×17×17bbox mm
>>> Polyhedra.tetrahedron(r=15)
V−E+F=2
Euler's formula holds for all five. The icosahedron's 12 vertices, 30 edges and 20 faces satisfy it — the test suite checks each solid.