/**
 * Canonical face lattice: the complete incidence structure of a polytope,
 * kept separate from the render-oriented `CellComplex`. `CellComplex`
 * stores homogeneous fixed-arity groups for rendering; a `FaceLattice`
 * stores every k-face with ragged arities plus the boundary maps between
 * consecutive layers. Wythoff-constructed polytopes are born as face
 * lattices and compiled down to cell complexes.
 */
/** Ragged array of index tuples: item i is data[offsets[i] … offsets[i+1]). */
export interface RaggedIndexBuffer {
    /** Length = itemCount + 1. */
    readonly offsets: Uint32Array;
    /** Concatenated item data. */
    readonly data: Uint32Array;
}
export declare function buildRagged(items: ReadonlyArray<ReadonlyArray<number>>): RaggedIndexBuffer;
export declare function raggedCount(buffer: RaggedIndexBuffer): number;
/** Item `i` as a subarray view (no copy). */
export declare function raggedItem(buffer: RaggedIndexBuffer, i: number): Uint32Array;
/** All k-faces of one dimension. */
export interface FaceLayer {
    /**
     * Vertex set of each face. For 2-faces the vertices are stored in
     * canonical cyclic (loop) order; other layers are order-insensitive.
     */
    readonly vertices: RaggedIndexBuffer;
    /** Orbit/type of each face under the constructing symmetry group. */
    readonly typeId: Uint16Array;
}
export interface FaceLattice {
    readonly rank: number;
    readonly vertexCount: number;
    /** layers[k] holds all k-faces, k = 1 … rank − 1. layers[0] is trivial. */
    readonly layers: ReadonlyArray<FaceLayer | undefined>;
    /**
     * boundary[k] maps each k-face to its incident (k−1)-face IDs.
     * boundary[0] and boundary[1] may be undefined (edge boundaries are
     * the edge vertex pairs themselves).
     */
    readonly boundary: ReadonlyArray<RaggedIndexBuffer | undefined>;
}
/** Face counts by dimension: [vertices, edges, 2-faces, …]. */
export declare function fVector(lattice: FaceLattice): number[];
/** Alternating-sum Euler characteristic of the boundary complex. */
export declare function eulerCharacteristic(lattice: FaceLattice): number;
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