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Axis of symmetry; isometric system

Short answer

An axis of symmetry is an imaginary line about which a crystal repeats its appearance 2, 3, 4, or 6 times in a full rotation. The isometric system has three equal axes at 90°, the highest symmetry, with forms like cube and octahedron; examples include galena and pyrite.

Define axis of symmetry with a figure. Describe the isometric crystal system.

Axis of symmetry

An axis of symmetry is an imaginary straight line through the centre of a crystal about which, when the crystal is rotated through 360°, the same appearance is repeated two, three, four or six times.

 Diad   (2-fold): 180 deg, repeats 2 times
 Triad  (3-fold): 120 deg, repeats 3 times
 Tetrad (4-fold):  90 deg, repeats 4 times
 Hexad  (6-fold):  60 deg, repeats 6 times

   Cube:   tetrad axis through face centres
           |
        +--|--+
        |  |  |
        +--|--+

Isometric (cubic) system

  • Three crystallographic axes of equal length, all at 90°: a=b=ca = b = c, α=β=γ=90∘\alpha = \beta = \gamma = 90^\circ.
  • Most symmetrical system; normal class has 9 planes, 13 axes (3 tetrad, 4 triad, 6 diad) and 1 centre of symmetry.
  • Forms: cube, octahedron, dodecahedron.
  • Minerals: galena, pyrite, fluorite, halite, garnet, diamond.

✓ Answer checked by Claude Opus 5.5 (high effort)

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