Radial · 2D · v1.0.0
Twelve-Fold Radial
Scroll to zoom, drag to pan, double-click to reset.
Mathematics
Geometric construction
12 points on a circle of radius R joined as the star polygon {12/step}, with spokes to the centre and the star's inner circle.
Symmetry: Dihedral D12.
Culture
Symbolic interpretation
Twelve-fold divisions echo the zodiac and calendar months.
Formulas
Available frequency mappings
- A · Direct ratio fᵢ = f₀ · rᵢ
- B · Power fᵢ = f₀ · rᵢ^α
- C · Logarithmic fᵢ = f₀ · 2^(k · log₂ rᵢ)
- D · Reference distance fᵢ = f₀ · (dᵢ / d_ref)^α
- E · Angular rᵢ = θᵢ / θ_ref ; fᵢ = f₀ · rᵢ^α
Units u
Coordinates
| id | x | y | z |
|---|---|---|---|
| P0 | 0.0000 | 0.0000 | 0.0000 |
| P1 | 0.0000 | 1.0000 | 0.0000 |
| P2 | -0.5000 | 0.8660 | 0.0000 |
| P3 | -0.8660 | 0.5000 | 0.0000 |
| P4 | -1.0000 | 0.0000 | 0.0000 |
| P5 | -0.8660 | -0.5000 | 0.0000 |
| P6 | -0.5000 | -0.8660 | 0.0000 |
| P7 | -0.0000 | -1.0000 | 0.0000 |
| P8 | 0.5000 | -0.8660 | 0.0000 |
| P9 | 0.8660 | -0.5000 | 0.0000 |
| P10 | 1.0000 | -0.0000 | 0.0000 |
| P11 | 0.8660 | 0.5000 | 0.0000 |
| P12 | 0.5000 | 0.8660 | 0.0000 |
Distances & angles
|P1P6|1.9319 u
|P0P1|1.0000 u
|P2P7|1.9319 u
|P0P2|1.0000 u
|P3P8|1.9319 u
|P0P3|1.0000 u
|P4P9|1.9319 u
|P0P4|1.0000 u
|P5P10|1.9319 u
|P0P5|1.0000 u
|P6P11|1.9319 u
|P0P6|1.0000 u
|P7P12|1.9319 u
|P0P7|1.0000 u
|P8P1|1.9319 u
|P0P8|1.0000 u
|P9P2|1.9319 u
|P0P9|1.0000 u
|P10P3|1.9319 u
|P0P10|1.0000 u
|P11P4|1.9319 u
|P0P11|1.0000 u
|P12P5|1.9319 u
|P0P12|1.0000 u
r(C0)1.0000 u
r(C1)0.2588 u
∠P6P1P00.2618 rad
∠P6P1P80.5236 rad
∠P0P1P80.2618 rad
∠P1P6P110.5236 rad
∠P1P6P00.2618 rad
∠P11P6P00.2618 rad
∠P1P0P20.5236 rad
∠P1P0P31.0472 rad
∠P1P0P41.5708 rad
∠P1P0P52.0944 rad
∠P1P0P62.6180 rad
∠P1P0P73.1416 rad
∠P1P0P82.6180 rad
∠P1P0P92.0944 rad
∠P1P0P101.5708 rad
∠P1P0P111.0472 rad
∠P1P0P120.5236 rad
∠P2P0P30.5236 rad
∠P2P0P41.0472 rad
∠P2P0P51.5708 rad
∠P2P0P62.0944 rad
∠P2P0P72.6180 rad
∠P2P0P83.1416 rad
∠P2P0P92.6180 rad
∠P2P0P102.0944 rad
∠P2P0P111.5708 rad
∠P2P0P121.0472 rad
∠P3P0P40.5236 rad
∠P3P0P51.0472 rad
∠P3P0P61.5708 rad
∠P3P0P72.0944 rad
∠P3P0P82.6180 rad
∠P3P0P93.1416 rad
∠P3P0P102.6180 rad
∠P3P0P112.0944 rad
∠P3P0P121.5708 rad
∠P4P0P50.5236 rad
∠P4P0P61.0472 rad
∠P4P0P71.5708 rad
∠P4P0P82.0944 rad
∠P4P0P92.6180 rad
∠P4P0P103.1416 rad
∠P4P0P112.6180 rad
∠P4P0P122.0944 rad
∠P5P0P60.5236 rad
∠P5P0P71.0472 rad
∠P5P0P81.5708 rad
∠P5P0P92.0944 rad
∠P5P0P102.6180 rad
∠P5P0P113.1416 rad
∠P5P0P122.6180 rad
∠P6P0P70.5236 rad
∠P6P0P81.0472 rad
∠P6P0P91.5708 rad
∠P6P0P102.0944 rad
∠P6P0P112.6180 rad
∠P6P0P123.1416 rad
∠P7P0P80.5236 rad
∠P7P0P91.0472 rad
∠P7P0P101.5708 rad
∠P7P0P112.0944 rad
∠P7P0P122.6180 rad
∠P8P0P90.5236 rad
∠P8P0P101.0472 rad
∠P8P0P111.5708 rad
∠P8P0P122.0944 rad
∠P9P0P100.5236 rad
∠P9P0P111.0472 rad
∠P9P0P121.5708 rad
∠P10P0P110.5236 rad
∠P10P0P121.0472 rad
∠P11P0P120.5236 rad
∠P7P2P00.2618 rad
∠P7P2P90.5236 rad
∠P0P2P90.2618 rad
∠P2P7P120.5236 rad
∠P2P7P00.2618 rad
∠P12P7P00.2618 rad
∠P8P3P00.2618 rad
∠P8P3P100.5236 rad
∠P0P3P100.2618 rad
∠P3P8P10.5236 rad
∠P3P8P00.2618 rad
∠P1P8P00.2618 rad
∠P9P4P00.2618 rad
∠P9P4P110.5236 rad
∠P0P4P110.2618 rad
∠P4P9P20.5236 rad
∠P4P9P00.2618 rad
∠P2P9P00.2618 rad
∠P10P5P00.2618 rad
∠P10P5P120.5236 rad
∠P0P5P120.2618 rad
∠P5P10P30.5236 rad
∠P5P10P00.2618 rad
∠P3P10P00.2618 rad
∠P6P11P40.5236 rad
∠P6P11P00.2618 rad
∠P4P11P00.2618 rad
∠P7P12P50.5236 rad
∠P7P12P00.2618 rad
∠P5P12P00.2618 rad
Derived ratios
r(C1)1.000000
∠P6P1P01.000000
∠P11P0P122.000000
|P0P2|3.863703
∠P6P0P84.000000
∠P6P0P96.000000
|P3P8|7.464102
∠P4P0P88.000000
∠P3P0P810.000000
∠P1P0P712.000000
f_i = f_0 × r_i · v1.0.0 · user-configured
Frequency derivation — centre distances
| id | r = d / R | exact (reference) | sources | f = f₀ × r |
|---|
Click a row to highlight its source points in the drawing. R = 1.0000 u. Exact forms are recognised reference values; the calculation itself is numeric. This mapping is a chosen design rule, not a law of nature.
My Archive
Saved generations from this symbol
Nothing saved yet for Twelve-Fold Radial.