How are the axes arranged in the hexagonal crystal system?

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In the hexagonal crystal system, the arrangement of crystallographic axes is defined by four axes:12

  • Horizontal axes: There are three axes of equal length (a1, a2, and a3) that lie in the same plane and intersect one another at angles of 120°.12
  • Vertical axis: The fourth axis (c) is of a different length and is oriented perpendicular to the plane containing the other three axes.12

This configuration is fundamental to the system's geometry, which is characterized by a primary axis of sixfold symmetry.2