examples/tesseract.py

   1 #!/usr/bin/env python3
   2
   3 # In geometry, the tesseract is the four-dimensional analog of the cube; the
   4 # tesseract is to the cube as the cube is to the square. Just as the surface of
   5 # the cube consists of 6 square faces, the hypersurface of the tesseract
   6 # consists of 8 cubical cells.
   7
   8 from linpy import Le, symbols
   9
  10
  11 x, y, z, t = symbols('x y z t')
  12
  13 tesseract = Le(0, x, 1) & Le(0, y, 1) & Le(0, z, 1) & Le(0, t, 1)
  14
  15
  16 def faces(polyhedron):
  17     for points in polyhedron.faces():
  18         face = points[0].aspolyhedron()
  19         face = face.convex_union(*[point.aspolyhedron()
  20                                    for point in points[1:]])
  21         yield face
  22
  23
  24 if __name__ == '__main__':
  25     print('Faces of tesseract\n\n  {}\n\nare:\n'.format(tesseract))
  26     for face in faces(tesseract):
  27         assert(len(face.vertices()) == 8)
  28         print('  {}'.format(face))