enumeratio

@enumeratio/polytope ​

Polytopes as face posets, not as vertex-coordinate lists: the permutahedron, simplex, cross-polytope, hypercube and associahedron, each stated purely as its combinatorics (enumerate a face, its dimension, its barycentre, vertex incidence), with the containment order and a projection into scene space derived from that. It declares no CE heads — it is a data layer other packages draw on to render or reason about these shapes.

Usage ​

Each polytope is a Polytope value keyed in POLYTOPES, and the polytope() helper fills in the derived face-poset contains order from the four primitives a shape states directly:

ts
import { PERMUTAHEDRON, POLYTOPES, scene } from "@enumeratio/polytope";

PERMUTAHEDRON.enumerate(3); // every set composition of {1, 2, 3} — the hexagon's 13 faces
POLYTOPES["cross-polytope"]; // by the name a page or attribute would spell

const points = scene(PERMUTAHEDRON, 4); // cast into an orthonormal basis of what it spans

scene.ts casts a face poset into ambient 3-space (or fewer, for a polytope that fills a proper subspace, or more — a higher-order shape scene-projects onto its leading axes), and render.ts turns a scene into 2D rings a caller can draw, given its own Project function.

Faces ​

Each polytope carries its faces as a distinct word shape:

  • PERMUTAHEDRON — set compositions of {1..n} (surjective label words; Fubini-counted)
  • SIMPLEX — nonempty subsets, as 0/1 words
  • CROSS_POLYTOPE / HYPERCUBE — the same signed-subset word over {−1, 0, +1}, read as dual to each other (spanned axes vs. fixed axes)
  • ASSOCIAHEDRON — noncrossing dissections of a convex polygon, as 0/1 words over its diagonals; Loday's coordinates

Pages ​