如何计算三维多边形的内角？

import math

def calculate_inner_angles(vertices):
    n = len(vertices)
    inner_angles = []

    for i in range(n):
        v1 = vertices[i]
        v2 = vertices[(i + 1) % n]
        v3 = vertices[(i + 2) % n]

        # 计算相邻边向量
        edge1 = [v2[0] - v1[0], v2[1] - v1[1], v2[2] - v1[2]]
        edge2 = [v3[0] - v2[0], v3[1] - v2[1], v3[2] - v2[2]]

        # 计算内角
        dot_product = edge1[0] * edge2[0] + edge1[1] * edge2[1] + edge1[2] * edge2[2]
        magnitude1 = math.sqrt(edge1[0] ** 2 + edge1[1] ** 2 + edge1[2] ** 2)
        magnitude2 = math.sqrt(edge2[0] ** 2 + edge2[1] ** 2 + edge2[2] ** 2)
        angle = math.acos(dot_product / (magnitude1 * magnitude2))

        inner_angles.append(angle)

    return inner_angles

# 示例多边形的顶点坐标
vertices = [(0, 0, 0), (1, 0, 0), (1, 1, 0), (0, 1, 0)]
inner_angles = calculate_inner_angles(vertices)

for i, angle in enumerate(inner_angles):
    print("内角{}: {:.2f}度".format(i+1, math.degrees(angle)))