How do spinel-group minerals arrange metal ions and oxygen atoms?

Spinel-group minerals, which follow the general chemical formula $A{B}_2{O}_4$, are characterized by a specific structural arrangement of their constituent atoms. In this structure, the oxygen atoms are organized in a cubic closest packing arrangement.123

Within this framework, the metal ions occupy the interstitial spaces—specifically the octahedral and tetrahedral sites—created by the close-packed oxygen atoms. The $A$ and $B$ positions are occupied by metal ions that may differ in type or oxidation state; most commonly, the $A$ site is occupied by a divalent ion (such as magnesium, iron, zinc, or manganese) and the $B$ site by a trivalent ion (such as aluminum, iron, or chromium). This structural configuration results in minerals that typically exhibit isometric symmetry.21