import { CellComplex } from '../geometry/cell-complex.js';
export interface DuoprismOptions {
    /** Vertex count of the first polygon (xy plane), ≥ 3. */
    p: number;
    /** Vertex count of the second polygon (zw plane), ≥ 3. */
    q: number;
    /** Circumradius of the p-gon. Default 1. */
    radius1?: number;
    /** Circumradius of the q-gon. Default 1. */
    radius2?: number;
}
/**
 * Builds the p,q-duoprism: the Cartesian product of two regular polygons,
 * one in the xy plane and one in the zw plane — the simplest uniform (but
 * not regular) polychoron family, and inherently 4D: no lower-dimensional
 * analogue is a product of two polygons.
 *
 * Structure: p·q vertices, 2pq edges, pq square faces (plus the polygon
 * faces of the prisms), and p + q prismatic cells — q p-gonal prisms and
 * p q-gonal prisms. Every vertex lies on the Clifford torus of radii
 * (radius1, radius2). The 4,4-duoprism with equal radii is a tesseract.
 *
 * Cells are decomposed into 6(pq − p − q) tetrahedra without helper
 * vertices (polygon fan × prism staircase), so the complex is sliceable.
 *
 * Only the pq squares are authored as 2-cells: a group carries one
 * `verticesPerCell`, so p-gons and q-gons cannot share the quad group.
 * The polygon faces are present in the tetrahedralization rather than as
 * cells of their own, which is why `cellCount(2)` reports pq and not the
 * polytope's full face count.
 *
 * @param options - Polygon orders and the two factor circumradii.
 *
 * @example
 * The 6,6-duoprism. The turn has to mix the two factors to show anything:
 * a rotation inside the xy or the zw plane alone is a symmetry of one
 * polygon, so the figure would slide within its own silhouette. Coupling
 * y to z instead trades the factors against each other, and the two
 * hexagonal rings visibly exchange roles:
 * ```ts
 * const duoprism = new ProjectedEdges3D(
 *   createDuoprism({ p: 6, q: 6 }),
 *   new PerspectiveProjection({ fromDim: 4, viewDistance: 4 })
 * );
 * scene.add(duoprism.object);
 *
 * onFrame((t) =>
 *   duoprism.update(
 *     new TransformN(4, rotationFromPlanes(4, [{ i: 1, j: 2, angle: t * 0.4 }]))
 *   )
 * );
 * ```
 *
 * @example
 * Taking both polygons square gives the tesseract's vertices and edges:
 * ```ts
 * const square = createDuoprism({ p: 4, q: 4 });
 * const tesseract = createHypercube({ dim: 4 });
 * square.vertexCount === tesseract.vertexCount; // true — 16
 * square.cellCount(1) === tesseract.cellCount(1); // true — 32
 * ```
 */
export declare function createDuoprism(options: DuoprismOptions): CellComplex;
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