Polygonal · 2D · v1.0.0
Octagon
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Mathematics
Geometric construction
Regular 8-gon inscribed in a circle of radius R; vertex k at angle 90° + 360°·k/8. Side length = 2R·sin(π/8).
Symmetry: Dihedral D8.
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 | -0.7071 | 0.7071 | 0.0000 |
| P3 | -1.0000 | 0.0000 | 0.0000 |
| P4 | -0.7071 | -0.7071 | 0.0000 |
| P5 | -0.0000 | -1.0000 | 0.0000 |
| P6 | 0.7071 | -0.7071 | 0.0000 |
| P7 | 1.0000 | -0.0000 | 0.0000 |
| P8 | 0.7071 | 0.7071 | 0.0000 |
Distances & angles
|P1P2|0.7654 u
|P2P3|0.7654 u
|P3P4|0.7654 u
|P4P5|0.7654 u
|P5P6|0.7654 u
|P6P7|0.7654 u
|P7P8|0.7654 u
|P8P1|0.7654 u
r(C0)1.0000 u
∠P2P1P82.3562 rad
∠P1P2P32.3562 rad
∠P2P3P42.3562 rad
∠P3P4P52.3562 rad
∠P4P5P62.3562 rad
∠P5P6P72.3562 rad
∠P6P7P82.3562 rad
∠P7P8P12.3562 rad
Derived ratios
|P2P3|1.000000
∠P2P1P81.000000
r(C0)1.306563
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