A mineral variety or a person associated with Benjamin or Benjaminism; can refer to a follower of Benjamin Disraeli or a mineral containing rare earths.
From Benjamin + -ite suffix (meaning 'follower of' or 'stone/mineral'). The suffix -ite creates nouns of affiliation or mineralogical varieties.
The -ite suffix is wonderfully versatile in English: it can mean you follow someone (Benjaminite = follower of Benjamin), or it can mean you're a rock (like dolomite or calcite), so the same word could refer to either a person or a mineral.
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