G.558 prism triangular base — Code

XII.7

Any prism which has a triangular base is divided into three pyramids equal to one another which have triangular bases.
F E D C B A 
"""Programmatic construction for Book XII, Proposition 7 (XII.7)."""

        from __future__ import annotations

        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure 0398.g1 using geometor.model."""
            model = Model("XII.7")

            # Points of the triangular prism ABC-DEF
            A = model.set_point(191.0, -175.0, classes=["given"], ID="A")
            B = model.set_point(62.0, -175.0, classes=["given"], ID="B")
            C = model.set_point(139.0, -140.0, classes=["given"], ID="C")
            D = model.set_point(152.0, -62.0, classes=["given"], ID="D")
            E = model.set_point(21.0, -62.0, classes=["given"], ID="E")
            F = model.set_point(98.0, -21.0, classes=["given"], ID="F")

            # Prism edges
            model.set_segment(A, B)
            model.set_segment(B, C)
            model.set_segment(C, A)
            model.set_segment(D, E)
            model.set_segment(E, F)
            model.set_segment(F, D)
            model.set_segment(A, D)
            model.set_segment(B, E)
            model.set_segment(C, F)

            # Joined diagonals
            model.set_segment(B, D)
            model.set_segment(E, C)
            model.set_segment(C, D)

            # Polygons (bases, parallelogram faces, and divided triangles)
            model.set_polygon([A, B, C])
            model.set_polygon([D, E, F])
            model.set_polygon([A, B, E, D])
            model.set_polygon([F, C, B, E])
            model.set_polygon([A, B, D])
            model.set_polygon([E, B, D])
            model.set_polygon([E, B, C])
            model.set_polygon([C, E, F])

            return model


        if __name__ == "__main__":
            construct_g1()