Step 2 of 4
Explore the Structure
Look at the construction, its points and its distances. Ratios between distances are what become frequencies.
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Geometry structure
The complete construction, whatever is shown in the drawing.
21
Points
shown
1
Circles
shown
30
Lines
shown
Measurements & ratios 5
Each length divided by the reference length gives a ratio r. These ratios become frequencies in the next step.
| Measurement | Length | Ratio r |
|---|---|---|
| |P8P10| | 0.7136 | 1.0000 |
| |P0P1| | 1.1547 | 1.6180 |
| |P0P3| | 1.6330 | 2.2882 |
| |P0P11| | 1.8683 | 2.6180 |
| |P0P7| | 2.0000 | 2.8025 |
Mathematical details
Vertices (±1,±1,±1) and cyclic permutations of (0, ±1/φ, ±φ), scaled to circumradius R.
Symmetry: Icosahedral Ih (order 120).
Symbolic interpretation
Plato associated it with the cosmos / aether.