G.554 pyramid triangular base — Code

XII.3

Any pyramid which has a triangular base is divided into two pyramids equal and similar to one another, similar to the whole and having triangular bases, and into two equal prisms; and the two prisms are greater than the half of the whole pyramid.

"""Programmatic construction for Book XII, Proposition 3 (XII.3).

        Pyramid ABCD with triangular base ABC and vertex D, bisected along its six
        edges at E, F, G, H, K, L into two equal and similar pyramids AEGH, HKLD and
        two equal prisms (EBFG, HK) and (GFC, HKL).
        """

        from __future__ import annotations

        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure 0382.g1 using geometor.model."""
            model = Model("XII.3")

            # Main vertices of pyramid ABCD
            D = model.set_point(128.0, -20.0, classes=["given"], ID="D")
            A = model.set_point(24.0, -198.0, classes=["given"], ID="A")
            B = model.set_point(210.0, -196.0, classes=["given"], ID="B")
            C = model.set_point(100.0, -142.0, classes=["given"], ID="C")

            # Midpoints of the 6 edges: E on AB, F on BC, G on CA, H on AD, K on DB, L on DC
            E = model.set_point(117.0, -197.0, ID="E")
            F = model.set_point(155.0, -169.0, ID="F")
            G = model.set_point(62.0, -170.0, ID="G")
            H = model.set_point(76.0, -109.0, ID="H")
            K = model.set_point(169.0, -108.0, ID="K")
            L = model.set_point(114.0, -81.0, ID="L")

            # Segments along main edges and sub-edges
            for p1, p2 in [
                (A, B), (A, E), (E, B),
                (B, C), (B, F), (F, C),
                (C, A), (C, G), (G, A),
                (A, D), (A, H), (H, D),
                (D, B), (D, K), (K, B),
                (D, C), (D, L), (L, C),
                (H, E), (E, G), (G, H),
                (H, K), (K, L), (L, H),
                (K, F), (F, G),
                (E, F), (E, K), (H, F),
            ]:
                model.set_segment(p1, p2)

            # Polygons (faces, bases, parallelograms, and solid outlines)
            for poly in [
                [A, B, C], [A, D, B], [D, B, C], [A, D, C],
                [A, E, H], [H, K, D], [A, H, G], [H, L, D],
                [E, H, G], [K, D, L], [A, E, G], [H, K, L],
                [G, F, C], [B, K, F], [E, B, F],
                [H, E, B, K], [E, B, F, G], [H, K, F, G], [K, F, C, L], [L, C, G, H],
            ]:
                model.set_polygon(poly)

            # Angles
            model.set_wedge(A, E, E, H)
            model.set_wedge(H, K, K, D)
            model.set_wedge(H, E, E, G)
            model.set_wedge(D, K, K, L)
            model.set_wedge(A, B, B, C)
            model.set_wedge(H, K, K, L)

            return model


        if __name__ == "__main__":
            construct_g1()