Task: Object-centric — perceptual counting
Question: Consider the shape that this python code draws:

------

import matplotlib.pyplot as plt
from matplotlib.patches import Polygon
import numpy as np

def draw_geometric_shape():
        """Plots a complex geometric shape consisting of 14 specific points and the13 triangles that connect them, based on a predefined set of Cartesian coordinates."""
        # Define the 14 points provided by the user.
        # The labels (A, B, C...) are based on the geometric description.
        # ULI/URI = Upper Left/Right Interior, LLI/LRI = Lower Left/Right Interior, CP = Central Point.
        points = {'A': (0, 3),'H': (-1, 2),'F': (1, 2),'ULI': (-3/7, 12/7),'URI': (3/7, 12/7),'CP': (0, 1.5),'I': (-2, 1),'G': (2, 1),'LLI': (-7/5, 4/5),'LRI': (7/5, 4/5),'B': (-3, 0),'D': (-1, 0),'E': (1, 0),'C': (3, 0)}
        
        # Define a new set of 12 triangles, arranged in pairs.
        # Each pair can be combined to form a single, larger triangle because# they share a side, and their other vertices lie on a straight line.
        # This arrangement makes it possible to form larger triangles from smaller ones.
        triangles = [
                # Group 0: the surrounding triangle,
                ('A', 'B', 'C'),
                # Group 1: These two triangles combine to form the larger triangle H-A-D# because points A, ULI, and D are collinear.
                ('H', 'A', 'ULI'),('H', 'ULI', 'D'),
                # Group 2: These two triangles combine to form the larger triangle F-A-E# because points A, URI, and E are collinear.
                ('F', 'A', 'URI'),('F', 'URI', 'E'),
                # Group 3: These two triangles combine to form the larger triangle I-B-F# because points B, LLI, and F are collinear.
                ('I', 'B', 'LLI'),('I', 'LLI', 'F'),
                # Group 4: These two triangles combine to form the larger triangle G-C-H# because points C, LRI, and H are collinear.
                ('G', 'C', 'LRI'),('G', 'LRI', 'H'),
                # Group 5: These two triangles combine to form the larger triangle D-I-E# because points I, LLI, and E are collinear.
                ('D', 'I', 'LLI'),('D', 'LLI', 'E'),
                # Group 6: These two triangles combine to form the larger triangle E-G-D# because points G, LRI, and D are collinear.
                ('E', 'G', 'LRI'),('E', 'LRI', 'D'),
        ]
        
        # --- Plotting Setup ---
        fig, ax = plt.subplots(figsize=(10, 9))
        ax.set_aspect('equal', adjustable='box')
        ax.grid(True, linestyle='--', alpha=0.6)
        
        # --- Draw the Triangles ---
        # Use a colormap for visually distinct triangle colors
        colors = plt.cm.viridis(np.linspace(0.1, 0.9, len(triangles)))
        for i, tri_labels in enumerate(triangles):
                # Get the coordinates for each vertex of the triangle
                vertices = [points[label] for label in tri_labels]
                
                # Create a Polygon patch
                polygon = Polygon(vertices, facecolor=colors[i], alpha=0.7, edgecolor='black', linewidth=1.2)
                
                # Add the patch to the plot
                ax.add_patch(polygon)
                
        # --- Draw the Points and Labels ---
        x_coords = [p[0] for p in points.values()]
        y_coords = [p[1] for p in points.values()]
        # Plot points on top of the triangles
        ax.scatter(x_coords, y_coords, color='red', s=50, zorder=5, label='Defined Points')
        
        # Add text labels for each point for clarity
        for label, (x, y) in points.items():
                ax.text(x + 0.08, y + 0.08, label, fontsize=12, fontweight='bold', ha='left', va='bottom')
        
        # --- Final Plot Customization ---
        ax.set_title(""Visualization of Geometric Points and Triangles"", fontsize=16)
        ax.set_xlabel(""X-coordinate"", fontsize=12)
        ax.set_ylabel(""Y-coordinate"", fontsize=12)
        
        # Set axis limits to provide some padding around the shape
        ax.set_xlim(-3.5, 3.5)
        ax.set_ylim(-0.5, 3.5)
        ax.legend()
        plt.tight_layout()
        plt.show()
        
if __name__ == '__main__':
        draw_geometric_shape()

-------

It is a triangle, with lines inside, that form other triangles and other shapes.
Compute the number of all triangles in this shape (including those ones which have unnamed vertices, and are a result of intersection of triangle edges). "

Solution: The correct answer is 26 total triangles. This is correct because the drawn shape is defined by the union of the plotted triangle edges, and counting all triangles (including composite triangles and those whose vertices are intersection points without labels) yields 26 distinct triangular regions/triangles that can be formed from the available line segments.

A common incorrect behaviour is counting only the 13 explicitly plotted triangles, missing larger composite triangles, or double-counting triangles that share the same boundary.