G.540 parallelepipedal solids base — Code

XI.30

Parallelepipedal solids which are on the same base and of the same height, and in which the extremities of the sides which stand up are not on the same segments, are equal.

"""Programmatic construction for Book XI, Proposition 30 (XI.30).

        Parallelepipedal solids CM and CN on the same base ACBL (AB) and of the same height,
        whose standing sides do not have their extremities on the same straight lines,
        compared via intermediate parallelepiped CP with top face OQRP.
        """

        from __future__ import annotations

        import sympy as sp
        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the three parallelepipeds CM, CN, CP for Book XI, Proposition 30."""
            model = Model("XI.30")

            # Top plane vertices
            N = model.set_point(sp.Rational(20, 100), sp.Rational(206, 100), classes=["given"], label="N")
            P = model.set_point(sp.Rational(91, 100), sp.Rational(206, 100), label="P")
            K = model.set_point(sp.Rational(188, 100), sp.Rational(206, 100), classes=["given"], label="K")
            R = model.set_point(sp.Rational(251, 100), sp.Rational(206, 100), label="R")

            M = model.set_point(sp.Rational(101, 100), sp.Rational(182, 100), classes=["given"], label="M")
            H = model.set_point(sp.Rational(261, 100), sp.Rational(182, 100), classes=["given"], label="H")

            G = model.set_point(sp.Rational(36, 100), sp.Rational(168, 100), classes=["given"], label="G")
            O = model.set_point(sp.Rational(107, 100), sp.Rational(168, 100), label="O")
            E = model.set_point(sp.Rational(204, 100), sp.Rational(168, 100), classes=["given"], label="E")
            Q = model.set_point(sp.Rational(267, 100), sp.Rational(168, 100), label="Q")

            F = model.set_point(sp.Rational(115, 100), sp.Rational(148, 100), classes=["given"], label="F")
            D = model.set_point(sp.Rational(275, 100), sp.Rational(148, 100), classes=["given"], label="D")

            # Base parallelogram ACBL
            L = model.set_point(sp.Rational(20, 100), sp.Rational(60, 100), classes=["given"], label="L")
            B = model.set_point(sp.Rational(188, 100), sp.Rational(60, 100), classes=["given"], label="B")
            A = model.set_point(sp.Rational(36, 100), sp.Rational(22, 100), classes=["given"], label="A")
            C = model.set_point(sp.Rational(204, 100), sp.Rational(22, 100), classes=["given"], label="C")

            # Top plane collinear lines and segments
            for p, q in [
                (N, R), (N, K), (G, Q), (G, E), (M, H), (F, D),
                (N, G), (K, E), (F, P), (F, M), (D, R), (D, H),
            ]:
                model.set_segment(p, q)

            # Standing edges
            for p, q in [
                (A, F), (A, G), (A, O),
                (L, M), (L, N), (L, P),
                (C, D), (C, E), (C, Q),
                (B, H), (B, K), (B, R),
                (A, C), (C, B), (B, L), (L, A),
            ]:
                model.set_segment(p, q)

            # Base and opposite faces
            model.set_polygon([A, C, B, L])
            model.set_polygon([F, D, H, M])
            model.set_polygon([O, Q, R, P])
            model.set_polygon([G, E, K, N])

            return model


        if __name__ == "__main__":
            construct_g1()