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and a 4-face is a 4-polytope. Furthermore, the following requirements must be met:
# Each cell must join exactly two 4-faces.
# Adjacent 4-faces are not in the same four-dimensional hyperplane.
# The figure is not a compound of other figures which meet the requirements.

Characteristics

The topology of any given 5-polytope is defined by its Betti numbers and torsion coefficients.

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