Platonic Solids Duality (2D)

Solid Pair

Dual Overlay

Rotation speed 0.15 rad/s

Tetrahedron is self-dual — swapping V and F returns the same solid.

Live Readout — Solid

Vertices (V)

Edges (E)

Faces (F)

Euler V−E+F

Live Readout — Dual

Dual V (= solid F)

Dual E (= solid E)

Dual F (= solid V)

Dual name

Tetrahedron

How it works

Every Platonic solid has a dual: put a new vertex at the center of each face, then connect two new vertices whenever their original faces shared an edge. The result is another polyhedron whose vertex count equals the original's face count, whose face count equals the original's vertex count, and whose edge count stays exactly the same.

This 2D diagram draws the solid's own graph flattened onto the plane (a Schlegel diagram — one face becomes the outer boundary, the rest nest inside it), then computes the dual graph directly from that same face list, so the swapped V/F numbers you see are calculated live, not looked up.

Tetrahedron ↔ tetrahedron (self-dual: 4 ↔ 4)
Cube ↔ octahedron (8 ↔ 6)
Dodecahedron ↔ icosahedron (20 ↔ 12)

Solid graph Dual graph