Polygonal · 2D · v1.0.0
Hexagon
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Mathematics
Geometric construction
Regular 6-gon inscribed in a circle of radius R; vertex k at angle 90° + 360°·k/6. Side length = 2R·sin(π/6).
Symmetry: Dihedral D6.
Culture
Symbolic interpretation
Regular polygons appear across architecture and ritual diagrams worldwide.
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 | -0.8660 | 0.5000 | 0.0000 |
| P3 | -0.8660 | -0.5000 | 0.0000 |
| P4 | -0.0000 | -1.0000 | 0.0000 |
| P5 | 0.8660 | -0.5000 | 0.0000 |
| P6 | 0.8660 | 0.5000 | 0.0000 |
Distances & angles
|P1P2|1.0000 u
|P2P3|1.0000 u
|P3P4|1.0000 u
|P4P5|1.0000 u
|P5P6|1.0000 u
|P6P1|1.0000 u
r(C0)1.0000 u
∠P2P1P62.0944 rad
∠P1P2P32.0944 rad
∠P2P3P42.0944 rad
∠P3P4P52.0944 rad
∠P4P5P62.0944 rad
∠P5P6P12.0944 rad
Derived ratios
|P4P5|1.000000
∠P2P3P41.000000
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