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X₁₉₂₀¶

CROSSSUM OF PU(12)

X₁₉₂₀ = perspector of Gemini triangle 31 and cross-triangle of ABC and Gemini triangle 31

X₁₉₂₀ (CROSSSUM OF PU(12)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1920 = CROSSSUM OF PU(12)."""

        from __future__ import annotations

        from pathlib import Path

        import sympy.geometry as spg
        from geometor.model import Model

        from geometor.etc.ops import (
            central_line,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            isotomic_conjugate,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01920(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1920 = CROSSSUM OF PU(12) on reference triangle ABC."""
            X_893 = eval_trilinear_point(model, A, B, C, 'a/(a**(2) + b*c)', ID="X_893", classes=["center"])
            X_1920 = isotomic_conjugate(model, A, B, C, X_893, ID="X_1920", classes=["selected", "target"])
            X_76 = eval_trilinear_point(model, A, B, C, '1/a**(3)', ID="X_76", classes=["center", "incident"])
            X_85 = eval_trilinear_point(model, A, B, C, 'b**(2)*c**(2)/(b + c - a)', ID="X_85", classes=["center", "incident"])
            central_line(model, X_76, X_85, 76, 85, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_561 = eval_trilinear_point(model, A, B, C, 'a **(- 4)', ID="X_561", classes=["center", "incident"])
            central_line(model, X_2, X_561, 2, 561, incident=True)
            X_310 = eval_trilinear_point(model, A, B, C, 'b**(3)*c**(3)/(b + c)', ID="X_310", classes=["center", "incident"])
            X_321 = eval_trilinear_point(model, A, B, C, '(b + c)*b**(2)*c**(2)', ID="X_321", classes=["center", "incident"])
            central_line(model, X_310, X_321, 310, 321, incident=True)
            return promote_point_to_top(model, X_1920)


        def build_model(
            sides: tuple[float, float, float] = (5.0, 6.0, 7.0),
            show_guides: bool = False,
        ) -> Model:
            """Build a `geometor.model.Model` for X_1920 on the given reference triangle."""
            model = create_model('X_1920 = CROSSSUM OF PU(12)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01920(model, A, B, C)
            return model


        if __name__ == "__main__":
            here = Path(__file__).resolve().parent
            model_acute = build_model((5.0, 6.0, 7.0))
            model_acute.save(str(here / "x-01920.json"))
            write_center_svg(
                model_acute,
                here / "x-01920.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1920¶

X₁₉₂₀¶