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intersection when used as an operation or volumetric operation between volumes or lines.

(not as a road intersection).

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For the set theory operation, there are a few terms as given in this Wikipedia article, including:

  • 共通部分｛きょうつうぶぶん｝
  • 共通集合｛きょうつうしゅうごう｝
  • 交差｛こうさ｝
  • 交わり｛まじわり｝
  • 積集合｛せきしゅうごう｝
  • 積｛せき｝

Although the article points out that 積 is also used to refer to the product of two sets, so 共通部分 is probably the preferred term. 共通 is also used for "in common" in other mathematical terms, e.g. if two triangles have the same height they might be referred to as 高さが共通.

As you can see in this page, the intersection of two or more 3D solids is referred to as 共通｛きょうつう｝部分｛ぶぶん｝の体積｛たいせき｝, and you would have similar terms for intersections of areas and other mathematical constructs.

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