Classical Convex Bodies Dataset

This dataset provides a reproducible benchmark of classical, origin-centred convex bodies in Euclidean dimensions 2 through 20.

The release contains 95,475 parameterised bodies in two complementary layers:

• CCBD-Core contains 475 canonical bodies, with 25 bodies in each dimension. It is intended as a small canonical reference set for formula checking and regression testing.
• CCBD-Instances contains 95,000 stratified benchmark instances, with 5,000 bodies in each dimension. It is intended for computational experiments, algorithm benchmarking, numerical studies, and machine-learning applications.

The dataset covers five body families: hypercubes, cross-polytopes, Euclidean balls, Lp balls for \(p=1,2,4,\infty\), and axis-aligned ellipsoids. Each main-table row records a stable identifier, dimension, construction parameters, geometric classifications, an exact-form volume expression, a double-precision volume evaluation, surface-area information, inradius, circumradius, diameter, and polar family.

Surface areas supplied by elementary formulae or direct standard special-function evaluation appear in the main tables. The remaining cases are covered by body-ID-keyed numerical sidecars containing fixed-seed randomized quasi-Monte Carlo estimates, standard errors, nominal 95% confidence intervals, sample counts, convergence information, and method provenance. All 55,858 released numerical estimates meet the predeclared maximum relative confidence-interval half-width of 0.2%. These intervals quantify statistical between-scramble uncertainty and are not deterministic worst-case bounds.

A deterministic stratified sidecar assigns the 95,000 instance rows to 76,000 training, 9,500 validation, and 9,500 test cases. CCBD-Core remains separate as a canonical reference set.

The release consists of five CSV data files, self-contained Python code for generating and validating the dataset, and accompanying documentation and reproducibility metadata.