import { CellComplex } from '../geometry/cell-complex.js';
export interface CrossPolytopeOptions {
    /** Ambient (and intrinsic) dimension; 4 gives the 16-cell. */
    dim: number;
    /** Circumradius (distance from center to each vertex). Default 1. */
    radius?: number;
    /**
     * Highest simplicial cell dimension to author, `1…dim-1` inclusive.
     * Requesting `dim` refuses by name: the cross-polytope's top cell is the
     * whole body with `2^dim` facets and is not a simplex, and authoring it as
     * one would be a lie. Default `min(dim - 1, 3)`, reproducing the historical
     * output byte-for-byte.
     *
     * For `k >= 2`, each group holds `C(dim, k+1) * 2^(k+1)` cells: ascending
     * axis subsets, lexicographic, then sign masks ascending (mask bit `j`
     * sends chosen axis `j` to its negative vertex). One vertex per distinct
     * axis, so no cell can contain an antipodal pair. The edge group predates
     * this family rule and keeps its frozen vertex-pair order — same cell set,
     * different order. Authored groups are combinatorial and **unoriented**
     * (render double-sided; oriented boundaries come from
     * `sectionSimplexGroupN`).
     */
    maxCellDimension?: number;
}
/**
 * Builds an n-dimensional cross-polytope (orthoplex): vertices at ±r·e_i.
 *
 * Vertices 0…n−1 are +e_i, vertices n…2n−1 are −e_i. Every vertex pair is
 * an edge except antipodal pairs: 2n(n−1) edges total.
 *
 * @param options - Ambient dimension and circumradius.
 *
 * @example
 * In four dimensions this is the 16-cell, dual to the tesseract — its 8
 * vertices answer to the tesseract's 8 cubic cells:
 * ```ts
 * const sixteenCell = createCrossPolytope({ dim: 4 });
 * sixteenCell.vertexCount; // 8
 * sixteenCell.cellCount(1); // 24 — all pairs but the 4 antipodal ones
 * ```
 *
 * @example
 * Dimension-complete authoring: the R5 cross-polytope's thirty-two simplicial
 * 4-facets — its whole boundary — while a requested top cell refuses by name,
 * because the body itself is not a simplex:
 * ```ts
 * const orthoplex = createCrossPolytope({ dim: 5, maxCellDimension: 4 });
 * log('boundary 4-facets', orthoplex.cellCount(4)); // 32 — C(5, 5) · 2⁵
 * ```
 *
 * @example
 * The 3D case is the octahedron, so the same call covers both:
 * ```ts
 * const octahedron = createCrossPolytope({ dim: 3 });
 * octahedron.vertexCount; // 6
 * ```
 */
export declare function createCrossPolytope(options: CrossPolytopeOptions): CellComplex;
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