Polyhedra · 3D · v1.0.0
Octahedron
Scroll to zoom, drag to pan, double-click to reset.
Mathematics
Geometric construction
Vertices (±1,0,0), (0,±1,0), (0,0,±1) scaled to circumradius R.
Symmetry: Octahedral Oh (order 48).
Culture
Symbolic interpretation
Plato associated it with air.
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 | 1.0000 | 0.0000 | 0.0000 |
| P1 | -1.0000 | 0.0000 | 0.0000 |
| P2 | 0.0000 | 1.0000 | 0.0000 |
| P3 | 0.0000 | -1.0000 | 0.0000 |
| P4 | 0.0000 | 0.0000 | 1.0000 |
| P5 | 0.0000 | 0.0000 | -1.0000 |
| P6 | 0.0000 | 0.0000 | 0.0000 |
Distances & angles
|P0P2|1.4142 u
|P0P3|1.4142 u
|P0P4|1.4142 u
|P0P5|1.4142 u
|P1P2|1.4142 u
|P1P3|1.4142 u
|P1P4|1.4142 u
|P1P5|1.4142 u
|P2P4|1.4142 u
|P2P5|1.4142 u
|P3P4|1.4142 u
|P3P5|1.4142 u
r(C0)1.0000 u
∠P2P0P31.5708 rad
∠P2P0P41.0472 rad
∠P2P0P51.0472 rad
∠P3P0P41.0472 rad
∠P3P0P51.0472 rad
∠P4P0P51.5708 rad
∠P0P2P11.5708 rad
∠P0P2P41.0472 rad
∠P0P2P51.0472 rad
∠P1P2P41.0472 rad
∠P1P2P51.0472 rad
∠P4P2P51.5708 rad
∠P0P3P11.5708 rad
∠P0P3P41.0472 rad
∠P0P3P51.0472 rad
∠P1P3P41.0472 rad
∠P1P3P51.0472 rad
∠P4P3P51.5708 rad
∠P0P4P11.5708 rad
∠P0P4P21.0472 rad
∠P0P4P31.0472 rad
∠P1P4P21.0472 rad
∠P1P4P31.0472 rad
∠P2P4P31.5708 rad
∠P0P5P11.5708 rad
∠P0P5P21.0472 rad
∠P0P5P31.0472 rad
∠P1P5P21.0472 rad
∠P1P5P31.0472 rad
∠P2P5P31.5708 rad
∠P2P1P31.5708 rad
∠P2P1P41.0472 rad
∠P2P1P51.0472 rad
∠P3P1P41.0472 rad
∠P3P1P51.0472 rad
∠P4P1P51.5708 rad
Derived ratios
r(C0)1.000000
∠P2P0P41.000000
|P0P2|1.414214
∠P2P0P31.500000
My Archive
Saved generations from this symbol
Nothing saved yet for Octahedron.