Preset group · Platonic solids
Platonic solids. The five elements, in sound.
The Platonic solids are the five bodies whose faces are all the same: tetrahedron, cube, octahedron, dodecahedron and icosahedron. In the Timaeus, Plato links them to the elements: fire to the tetrahedron, air to the octahedron, water to the icosahedron and earth to the cube. He keeps the dodecahedron for the universe as a whole; later tradition called it aether, the fifth element.
Sacred geometry sees them as the pieces the world is built from. Here they're six presets: the five solids and Metatron's Cube, which the tradition says contains them all.
The formulas and the figures in the code.
Each solid plays at its number of vertices times 108, the sacred number of Hinduism, Buddhism and Jainism (prayer malas have 108 beads). Tetrahedron: 4 vertices × 108 = 432 Hz. Octahedron: 6 × 108 = 648 Hz. Cube: 8 × 108 = 864 Hz. Icosahedron: 12 × 108 = 1296 Hz. Dodecahedron: 20 × 108 = 2160 Hz.
The tetrahedron lands right on 432 Hz, The One. Metatron doesn't follow the formula: it plays at 852 Hz, as in the Solfeggio series.
One line per preset.
- Tetrahedron · Fire
432 Hz
Tetrahedron, fire. Four vertices, 432 Hz.
Physical figure (8, 4) · Symbolic layer: Tetrahedron · Fire
- Octahedron · Air
648 Hz
Octahedron, air. Six vertices, 648 Hz.
Physical figure (10, 4) · Symbolic layer: Octahedron · Air
- Icosahedron · Water
1296 Hz
Icosahedron, water. Twelve vertices, 1296 Hz.
Physical figure (14, 6) · Symbolic layer: Icosahedron · Water
- Cube · Earth
864 Hz
Cube, earth. Eight vertices, 864 Hz. For touching ground.
Physical figure (12, 4) · Symbolic layer: Cube · Earth
- Dodecahedron · Aether
2160 Hz
Dodecahedron, aether. Twenty vertices, 2160 Hz, the highest.
Physical figure (14, 14) + (18, 8) · Symbolic layer: Dodecahedron · Ether
- Metatron · holds all five
852 Hz
Metatron's Cube, which the tradition says contains all five, at 852 Hz.
Physical figure (12, 4) + (12, 2) · Symbolic layer: Metatron's Cube
Tab. 01 · Plate figure calculated by the app's core (cym.core.js) for each frequency: a square plate driven at the center, f = 5.5·(n² + m²) Hz. Two modes = the plate answers with both.
The physical figure and the symbolic layer.
In Chladni, the tetrahedron draws mode (8, 4), the cube mode (12, 4) and the dodecahedron, the highest, a blend of modes (14, 14) and (18, 8). The square plate doesn't draw the solid: it draws the figure of that frequency.
The solid is the layer, in perspective and turning slowly: a symbolic layer, an association from the tradition, not calculated from the sound. In Metatron's Cube, strictly speaking, only the cube, the tetrahedron and the octahedron show up cleanly; the dodecahedron and the icosahedron aren't exact in its flat drawing.
What people ask about this group.
Q1What are the Platonic solids?
The five regular polyhedra: tetrahedron, cube, octahedron, dodecahedron and icosahedron. All their faces are the same and the same number meet at each vertex. Plato described them in the Timaeus.
Q2Which element is each solid?
According to the Timaeus, the tetrahedron is fire, the octahedron air, the icosahedron water and the cube earth. The dodecahedron is the universe; later tradition called it aether.
Q3Why multiply by 108?
Because 108 is a sacred number in Hinduism, Buddhism and Jainism. Times the vertices of each solid it gives its frequency: the tetrahedron, with 4, plays at 432 Hz. It's a symbolic choice, not a law of physics.
Q4Does Metatron's Cube contain the five solids?
That's what the tradition says. In its flat drawing the cube, the tetrahedron and the octahedron show up cleanly; the dodecahedron and the icosahedron aren't exact.