icosahedron.py hinzugefügt

icosahedron.py

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+import numpy as np
+import matplotlib.pyplot as plt
+from mpl_toolkits.mplot3d.art3d import Poly3DCollection
+import time
+
+def icosahedron_vertices(radius=1):
+    phi = (1 + np.sqrt(5)) / 2
+    
+    vertices = np.array([
+        [-1,  phi, 0],
+        [ 1,  phi, 0],
+        [-1, -phi, 0],
+        [ 1, -phi, 0],
+        
+        [0, -1,  phi],
+        [0,  1,  phi],
+        [0, -1, -phi],
+        [0,  1, -phi],
+        
+        [ phi, 0, -1],
+        [ phi, 0,  1],
+        [-phi, 0, -1],
+        [-phi, 0,  1]
+    ])
+    
+    vertices /= np.linalg.norm(vertices, axis=1).max()
+    vertices *= radius
+    
+    return vertices
+
+def plot_icosahedron(vertices, face_colors):
+    fig = plt.figure()
+    ax = fig.add_subplot(111, projection='3d')
+
+    faces = [
+        [vertices[0], vertices[11], vertices[5]],
+        [vertices[0], vertices[5], vertices[1]],
+        [vertices[0], vertices[1], vertices[7]],
+        [vertices[0], vertices[7], vertices[10]],
+        [vertices[0], vertices[10], vertices[11]],
+        
+        [vertices[1], vertices[5], vertices[9]],
+        [vertices[5], vertices[11], vertices[4]],
+        [vertices[11], vertices[10], vertices[2]],
+        [vertices[10], vertices[7], vertices[6]],
+        [vertices[7], vertices[1], vertices[8]],
+        
+        [vertices[3], vertices[9], vertices[4]],
+        [vertices[3], vertices[4], vertices[2]],
+        [vertices[3], vertices[2], vertices[6]],
+        [vertices[3], vertices[6], vertices[8]],
+        [vertices[3], vertices[8], vertices[9]],
+        
+        [vertices[4], vertices[9], vertices[5]],
+        [vertices[2], vertices[4], vertices[11]],
+        [vertices[6], vertices[2], vertices[10]],
+        [vertices[8], vertices[6], vertices[7]],
+        [vertices[9], vertices[8], vertices[1]]
+    ]
+    
+    for i, face in enumerate(faces):
+        poly3d = [face]
+        poly3dcollection = Poly3DCollection(poly3d, facecolors=face_colors[i], linewidths=1, edgecolors='grey', alpha=0.7)
+        ax.add_collection3d(poly3dcollection)
+  
+    ax.set_xlim(-1, 1)
+    ax.set_ylim(-1, 1)
+    ax.set_zlim(-1, 1)
+
+    ax.axis("off")
+
+if __name__ == '__main__':
+    
+    icosahedron_radius = 1.0
+    icosahedron_vertices = icosahedron_vertices(icosahedron_radius)
+    
+    face_colors = [[0.1,0.1,0.1],[0.1,0.1,0.1],[0.1,0.1,0.1],[0.1,0.1,0.1],[0.1,0.1,0.1],
+                   [0.1,0.1,0.1],[0.1,0.1,0.1],[0.1,0.1,0.1],[0.1,0.1,0.1],[0.1,0.1,0.1],
+                   [0.1,0.1,0.1],[0.1,0.1,0.1],[0.1,0.1,0.1],[0.1,0.1,0.9],[0.1,0.1,0.1],#<- vorletztes blau
+                   [0.1,0.1,0.1],[0.1,0.1,0.1],[0.1,0.1,0.1],[0.1,0.1,0.1],[0.1,0.1,0.1]]
+    
+    if len(face_colors) != 20:
+        raise ValueError("You must specify colors for all 20 faces of the icosahedron.")
+    
+    plot_icosahedron(icosahedron_vertices, face_colors)
+    plt.show()