<｜begin▁of▁sentence｜>### Instruction:
Given a set of points [(0, 0), (1, 1), (2, 0), (1, -1), (0.5, 0.2)], how can you use the 'ConvexHull' function from scipy.spatial to calculate the convex hull and retrieve both the indices and the coordinates of the hull's corners?
### Response:
from scipy.spatial import ConvexHull
import numpy as np

# Define a set of points
points = np.array([[0, 0], [1, 1], [2, 0], [1, -1], [0.5, 0.2]])

# Calculate the convex hull of the point set
hull = ConvexHull(points)

# Get the indices of the hull vertices
corner_indices = hull.vertices

# If we need the coordinates of the hull corners
corner_coords = points[hull.vertices]

print(f'Corners Indices: {corner_indices}')
print(f'Corners Coordinates: {corner_coords}')
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