BTC Polychoron is a data-sculpture generated from Bitcoin market history by embedding the time series into R⁴, computing the 4D convex hull boundary (a polychoron “envelope”), then mapping it into 3D via stereographic projection. The result is a single continuous object whose surface encodes extremes/regime structure rather than average behavior: the hull captures the outer geometry of the dataset and turns it into a readable form. Topology 4D edge (ConvexHull in R⁴): V = 28,432 (vertex hull 4D) E = 201,583 F = 346,302 (triangular faces) C = 173,151 (tetrahedric cells 4D) χ₄ = V − E + F − C = 0 This model contains 500,000 vertices and 346,302 faces. Vertex color encodes the original data channels: R ≈ 4th-dimension depth (w), G ≈ normalized price, B ≈ time gradient, producing a chromatic field that reveals trajectory and regime shifts while rotating. Built procedurally (Python) as a true geometry pipeline, not a texture trick. Period: 2017-08-17 → 2021-08-20 (UTC) Price Range: ~$2,919 → ~$64,577