Catalan Solids · 3D
Rhombic Triacontahedron
Thirty golden rhombi
Thirty rhombi, each with diagonals in the golden ratio. Its corners combine an icosahedron and a dodecahedron, so the two golden solids share one skin.
- Vertices
- 12 + 20
- Edges
- 60
- Faces
- 30
- Diagonals
- 1 : φ
Turn it in your hands, strike it to hear the chord of its edges, slice it with a plane.
Facts
- Each face is a golden rhombus: its long diagonal is φ times the short one.
- Its 12 five-fold corners are an icosahedron, its 20 three-fold corners a dodecahedron.
- It is the dual of the icosidodecahedron, and the 3D shadow of a six-dimensional cube.
- Its faces are the thirty directions of the icosahedral quasicrystal, the 3D Penrose tiling.
- Strike it: its two lowest tones stand in the golden ratio.
History and meaning
Kepler drew it in Harmonices Mundi (1619). Dice with thirty faces are made in this shape, and it is the frame of many modern golden-ratio sculptures.
Across the dimensions
- Dual Icosidodecahedron
