import { CellComplex } from '../geometry/cell-complex.js';
export interface SimplexOptions {
    /** Intrinsic (and ambient) dimension; 4 gives the 5-cell. */
    dim: number;
    /** Edge length. Default 1. */
    edgeLength?: number;
    /**
     * Highest cell dimension to author, `1…dim` inclusive — `dim` is the top
     * simplex itself, one cell naming every vertex, which is what the RN
     * section path consumes. Default `min(dim, 3)`, reproducing the historical
     * output byte-for-byte; each `k` in range emits one group of all
     * `C(dim+1, k+1)` ascending-index `(k+1)`-subsets, lexicographic.
     *
     * Authored groups are combinatorial and **unoriented**: ascending-index
     * order is not boundary-coherent (shared faces double rather than cancel),
     * so render double-sided, and derive oriented boundaries from
     * `sectionSimplexGroupN`, which computes them from geometry.
     */
    maxCellDimension?: number;
}
/**
 * Builds a regular n-simplex (n+1 vertices) centered at the origin in ℝⁿ.
 *
 * Construction: take the n+1 standard basis vectors of R^(n+1) — which form
 * a regular simplex with edge length √2 in the hyperplane orthogonal to the
 * all-ones vector — recenter on their centroid, express them in an
 * orthonormal basis of that hyperplane (modified Gram–Schmidt), and scale.
 *
 * @param options - Intrinsic dimension and target edge length.
 *
 * @example
 * The 5-cell — the 4D tetrahedron, and the smallest polychoron there is:
 * ```ts
 * const fiveCell = createSimplex({ dim: 4 });
 * fiveCell.vertexCount; // 5
 * fiveCell.cellCount(1); // 10 — every pair of vertices is an edge
 * ```
 *
 * @example
 * Dimension-complete authoring: the R5 simplex with every face family up to
 * its six simplicial 4-facets and the top cell itself — which is exactly what
 * a chained RN section consumes:
 * ```ts
 * const body = createSimplex({ dim: 5, maxCellDimension: 5 });
 * log('tets', body.cellCount(3)); // 15 — C(6, 4)
 * log('4-facets', body.cellCount(4)); // 6 — C(6, 5), new above the default
 * log('top cell', body.cellCount(5)); // 1 — the simplex itself
 * ```
 *
 * @example
 * Every simplex is its own tetrahedralization, so this projects and
 * slices without any preparation:
 * ```ts
 * const fiveCell = new ProjectedEdges3D(
 *   createSimplex({ dim: 4 }),
 *   new PerspectiveProjection({ fromDim: 4, viewDistance: 4 })
 * );
 * scene.add(fiveCell.object);
 *
 * onFrame((t) =>
 *   fiveCell.update(
 *     new TransformN(4, rotationFromPlanes(4, [{ i: 0, j: 3, angle: t * 0.5 }]))
 *   )
 * );
 * ```
 */
export declare function createSimplex(options: SimplexOptions): CellComplex;
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