p31ca · icosa shell mathematics

Subdivided icosa (cockpit shell)

The Sovereign Cockpit builds a spherical polyhedron by starting from a regular icosahedron, projecting vertices to a sphere, then repeatedly splitting each triangular face into four and pushing new midpoints to the same radius. That matches common graphics “geodesic” spheres; it is not a full structural (chord / hub) schedule for a physical dome, and it is not proprietary theme-park panel data.

Parameters aligned with the live page: radius = 3.5, subdivisions = 2 (same as buildIcosaSphereDome in src/lib/dome/icosphere-geometry.ts).

Vertices

162

Faces (triangles)

320

Undirected edges

480

Edge length min

0.9657

Edge length max

1.1372

Edge length mean

1.0477

Coef. of variation (σ/μ)

0.064512

Unique chord buckets (rounded 1e-3): 0.966, 0.999, 1.095, 1.124, 1.137

Observatory (static) uses [email protected] and IcosahedronGeometry(r, 2)—same family, different implementation path. Compare before assuming identical edge graphs.

Operator Larmor copy (p31-constants physics.larmorHz): 863Hz