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For a non‐empty polyhedral set    P  ⊂   R  d    , let    F  (  P  )    denote the set of faces of   P  , and let    N  (  P  ,  F  )    be the normal cone of   P   at the non‐empty face    F  ∊  F  (  P  )   . We prove the identity∑  F  ∈  F    (  P  )    ⁡    (  −  1  )    dim  ⁡  F   F  −  N  (  P  ,  F  )    =1if P is bounded  ,0if P is unbounded and line‐free  .Previously, this formula was known to hold everywhere outside some exceptional set of Lebesgue measure 0 or for polyhedral cones. The case of a not necessarily line‐free polyhedral set is also covered by our general theorem.

AN INCLUSION–EXCLUSION IDENTITY FOR NORMAL CONES OF POLYHEDRAL SETS