Polyhedra · 3D · v1.0.0
Cube (Hexahedron)
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Mathematics
Geometric construction
Vertices (±1, ±1, ±1) scaled to circumradius R.
Symmetry: Octahedral Oh (order 48).
Culture
Symbolic interpretation
Plato associated it with earth.
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 | 0.5774 | 0.5774 | 0.5774 |
| P1 | 0.5774 | 0.5774 | -0.5774 |
| P2 | 0.5774 | -0.5774 | 0.5774 |
| P3 | 0.5774 | -0.5774 | -0.5774 |
| P4 | -0.5774 | 0.5774 | 0.5774 |
| P5 | -0.5774 | 0.5774 | -0.5774 |
| P6 | -0.5774 | -0.5774 | 0.5774 |
| P7 | -0.5774 | -0.5774 | -0.5774 |
| P8 | 0.0000 | 0.0000 | 0.0000 |
Distances & angles
|P0P1|1.1547 u
|P0P2|1.1547 u
|P0P4|1.1547 u
|P1P3|1.1547 u
|P1P5|1.1547 u
|P2P3|1.1547 u
|P2P6|1.1547 u
|P3P7|1.1547 u
|P4P5|1.1547 u
|P4P6|1.1547 u
|P5P7|1.1547 u
|P6P7|1.1547 u
r(C0)1.0000 u
∠P1P0P21.5708 rad
∠P1P0P41.5708 rad
∠P2P0P41.5708 rad
∠P0P1P31.5708 rad
∠P0P1P51.5708 rad
∠P3P1P51.5708 rad
∠P0P2P31.5708 rad
∠P0P2P61.5708 rad
∠P3P2P61.5708 rad
∠P0P4P51.5708 rad
∠P0P4P61.5708 rad
∠P5P4P61.5708 rad
∠P1P3P21.5708 rad
∠P1P3P71.5708 rad
∠P2P3P71.5708 rad
∠P1P5P41.5708 rad
∠P1P5P71.5708 rad
∠P4P5P71.5708 rad
∠P2P6P41.5708 rad
∠P2P6P71.5708 rad
∠P4P6P71.5708 rad
∠P3P7P51.5708 rad
∠P3P7P61.5708 rad
∠P5P7P61.5708 rad
Derived ratios
r(C0)1.000000
∠P1P0P21.000000
|P0P1|1.154701
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