import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d.art3d import Poly3DCollection

def plot_3d_figure():
    fig = plt.figure(figsize=(10, 8))
    ax = fig.add_subplot(111, projection='3d')

    # Define the vertices of the inscribed tetrahedron
    # The bounding box is a 6x6x6 cube
    v1 = [0, 0, 6]  # Top-left-front
    v2 = [6, 0, 0]  # Bottom-right-front
    v3 = [0, 6, 0]  # Bottom-left-back
    v4 = [6, 6, 6]  # Top-right-back

    # Define the 4 triangular faces of the tetrahedron
    faces = [
        [v1, v2, v3],
        [v1, v2, v4],
        [v1, v3, v4],
        [v2, v3, v4]
    ]

    # Create the 3D polygon collection
    poly3d = Poly3DCollection(faces, facecolors='#4C99D1', linewidths=1.5, edgecolors='black', alpha=0.85)
    ax.add_collection3d(poly3d)

    # Draw the bounding box (cube) with dashed lines for better visualization context
    cube_vertices = [
        [0,0,0], [6,0,0], [6,6,0], [0,6,0],
        [0,0,6], [6,0,6], [6,6,6], [0,6,6]
    ]
    cube_edges = [
        (0,1), (1,2), (2,3), (3,0), # bottom
        (4,5), (5,6), (6,7), (7,4), # top
        (0,4), (1,5), (2,6), (3,7)  # vertical
    ]
    for edge in cube_edges:
        p1 = cube_vertices[edge[0]]
        p2 = cube_vertices[edge[1]]
        ax.plot([p1[0], p2[0]], [p1[1], p2[1]], [p1[2], p2[2]], color='gray', linestyle='--', linewidth=1, alpha=0.4)

    # Set axes limits
    ax.set_xlim([0, 6])
    ax.set_ylim([0, 6])
    ax.set_zlim([0, 6])

    # Set labels
    ax.set_xlabel('X (Width)')
    ax.set_ylabel('Y (Depth)')
    ax.set_zlabel('Z (Height)')

    # Set viewing angle to clearly see the shape
    ax.view_init(elev=25, azim=-55)

    # Force equal proportions for the axes
    ax.set_box_aspect([1, 1, 1])
    
    plt.title("3D Reconstruction: Regular Tetrahedron Inscribed in a Cube", fontsize=14, pad=20)
    plt.tight_layout()
    plt.show()

if __name__ == "__main__":
    plot_3d_figure()