Step 2 of 4
Explore the Structure
Look at the construction, its points and its distances. Ratios between distances are what become frequencies.
Scroll or pinch to zoom, drag to move.
Geometry structure
The complete construction, whatever is shown in the drawing.
13
Points
shown
1
Circles
shown
30
Lines
shown
Measurements & ratios 3
Each length divided by the reference length gives a ratio r. These ratios become frequencies in the next step.
| Measurement | Length | Ratio r |
|---|---|---|
| |P0P2| | 1.0515 | 1.0000 |
| |P0P5| | 1.7013 | 1.6180 |
| |P0P3| | 2.0000 | 1.9021 |
Mathematical details
Vertices: cyclic permutations of (0, ±1, ±φ), φ = (1+√5)/2, scaled to circumradius R.
Symmetry: Icosahedral Ih (order 120).
Symbolic interpretation
Plato associated it with water.