Transformations · 3D

Dodecahedron to Icosahedron

Truncation through the golden solids

The golden version of the same story. Cut the dodecahedron’s corners and its pentagons become decagons, then pentagons again at the halfway icosidodecahedron, while triangles grow into the hexagons of the football and at last the icosahedron.

Solids: 5
Archimedean: 3
Symmetries: 120

Open in SacredForm

Turn it in your hands, strike it to hear the chord of its edges, slice it with a plane.

Facts

For regular decagons the first cut runs 1/(φ√5) ≈ 0.276 of the way along each edge.
At two thirds of the way to the icosahedron it passes through the truncated icosahedron: the football, and carbon-60.
The dodecahedron and the icosahedron are duals: cut either all the way and you reach the other.
At the midpoint the icosidodecahedron’s edges form six great decagons.