User-generated · 2D · v1.0.0
Custom Construction
Scroll to zoom, drag to pan, double-click to reset.
Mathematics
Geometric construction
Your configuration: k iterations of n-point star polygons {n/step} with halving radius, plus c circles of radius R/2 around the centre.
Symmetry: Dihedral Dn (by construction).
Culture
Symbolic interpretation
User-defined geometry; no tradition implied.
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 | -0.6428 | 0.7660 | 0.0000 |
| P3 | -0.9848 | 0.1736 | 0.0000 |
| P4 | -0.8660 | -0.5000 | 0.0000 |
| P5 | -0.3420 | -0.9397 | 0.0000 |
| P6 | 0.3420 | -0.9397 | 0.0000 |
| P7 | 0.8660 | -0.5000 | 0.0000 |
| P8 | 0.9848 | 0.1736 | 0.0000 |
| P9 | 0.6428 | 0.7660 | 0.0000 |
| P10 | -0.1710 | 0.4698 | 0.0000 |
| P11 | -0.4330 | 0.2500 | 0.0000 |
| P12 | -0.4924 | -0.0868 | 0.0000 |
| P13 | -0.3214 | -0.3830 | 0.0000 |
| P14 | -0.0000 | -0.5000 | 0.0000 |
| P15 | 0.3214 | -0.3830 | 0.0000 |
| P16 | 0.4924 | -0.0868 | 0.0000 |
| P17 | 0.4330 | 0.2500 | 0.0000 |
| P18 | 0.1710 | 0.4698 | 0.0000 |
| P19 | -0.1607 | 0.1915 | 0.0000 |
| P20 | -0.2462 | 0.0434 | 0.0000 |
| P21 | -0.2165 | -0.1250 | 0.0000 |
| P22 | -0.0855 | -0.2349 | 0.0000 |
| P23 | 0.0855 | -0.2349 | 0.0000 |
| P24 | 0.2165 | -0.1250 | 0.0000 |
| P25 | 0.2462 | 0.0434 | 0.0000 |
| P26 | 0.1607 | 0.1915 | 0.0000 |
| P27 | 0.0000 | 0.2500 | 0.0000 |
| P28 | 0.0000 | 0.5000 | 0.0000 |
| P29 | -0.4330 | -0.2500 | 0.0000 |
| P30 | 0.4330 | -0.2500 | 0.0000 |
Distances & angles
|P1P3|1.2856 u
|P2P4|1.2856 u
|P3P5|1.2856 u
|P4P6|1.2856 u
|P5P7|1.2856 u
|P6P8|1.2856 u
|P7P9|1.2856 u
|P8P1|1.2856 u
|P9P2|1.2856 u
|P10P12|0.6428 u
|P11P13|0.6428 u
|P12P14|0.6428 u
|P13P15|0.6428 u
|P14P16|0.6428 u
|P15P17|0.6428 u
|P16P18|0.6428 u
|P17P10|0.6428 u
|P18P11|0.6428 u
|P19P21|0.3214 u
|P20P22|0.3214 u
|P21P23|0.3214 u
|P22P24|0.3214 u
|P23P25|0.3214 u
|P24P26|0.3214 u
|P25P27|0.3214 u
|P26P19|0.3214 u
|P27P20|0.3214 u
r(C0)0.5000 u
r(C1)0.5000 u
r(C2)0.5000 u
r(C3)0.5000 u
r(C4)0.5000 u
r(C5)0.5000 u
r(C6)1.0000 u
|C0C1|0.5000 u
|C0C2|0.8660 u
|C0C3|1.0000 u
|C0C4|0.8660 u
|C0C5|0.5000 u
|C0C6|0.5000 u
|C1C2|0.5000 u
|C1C3|0.8660 u
|C1C4|1.0000 u
|C1C5|0.8660 u
|C1C6|0.5000 u
|C2C3|0.5000 u
|C2C4|0.8660 u
|C2C5|1.0000 u
|C2C6|0.5000 u
|C3C4|0.5000 u
|C3C5|0.8660 u
|C3C6|0.5000 u
|C4C5|0.5000 u
|C4C6|0.5000 u
|C5C6|0.5000 u
∠P3P1P81.7453 rad
∠P1P3P51.7453 rad
∠P4P2P91.7453 rad
∠P2P4P61.7453 rad
∠P3P5P71.7453 rad
∠P4P6P81.7453 rad
∠P5P7P91.7453 rad
∠P6P8P11.7453 rad
∠P7P9P21.7453 rad
∠P12P10P171.7453 rad
∠P10P12P141.7453 rad
∠P13P11P181.7453 rad
∠P11P13P151.7453 rad
∠P12P14P161.7453 rad
∠P13P15P171.7453 rad
∠P14P16P181.7453 rad
∠P15P17P101.7453 rad
∠P16P18P111.7453 rad
∠P21P19P261.7453 rad
∠P19P21P231.7453 rad
∠P22P20P271.7453 rad
∠P20P22P241.7453 rad
∠P21P23P251.7453 rad
∠P22P24P261.7453 rad
∠P23P25P271.7453 rad
∠P24P26P191.7453 rad
∠P25P27P201.7453 rad
Derived ratios
|P22P24|1.000000
∠P16P18P111.000000
|C3C4|1.555724
|P14P16|2.000000
|C3C5|2.694593
r(C6)3.111448
|P5P7|4.000000
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 |
|---|---|---|---|---|
| R1 | 0.500000000 | 1/2 | |P28P11| |P28P17| |P28P0| … | 220 × 1/2 = 110.000 Hz |
| R2 | 0.866025404 | √3/2 | |P28P29| |P28P30| |P11P14| … | 220 × √3/2 = 190.526 Hz |
| R3 | 1.000000000 | 1 | |P28P14| |P11P30| |P29P17| | 220 × 1 = 220.000 Hz |
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 Custom Construction.