A　convex　polyhedron　classifier　that　encloses　the　minority　class　using　a　combination　of　hyperplanes　is　potentially　effective　in　imbalanced　classification.　To　construct　an　easy-to-use　convex　polyhedron　classifier,　this　paper　first　presents　a　theoretical　foundation　for　determining　whether　a　point　is　within　the　convex　hull　of　a　finite　point　set.　This　foundation　corresponds　to　a　geometric　method　in　which　the　result　is　expressed　as　a　separating　hyperplane.　If　the　given　point　and　the　given　convex　hull　are　located　on　either　side　of　the　learned　hyperplane,　this　indicates　that　the　point　is　outside　of　the　convex　hull.　Otherwise,　the　conclusion　that　the　point　is　within　the　convex　hull　can　be　obtained.　As　a　generalization　of　the　geometric　method,　a　convex　polyhedron　classifier　is　further　proposed　for　binary　classification.　If　two　finite　point　sets　are　polyhedrally　separable,　a　series　of　hyperplanes　can　be　learned　as　a　combined　(piecewise　linear)　classifier,　which　surrounds　a　point　set　that　is　inside　using　a　convex　polyhedron　and　excludes　the　other　point　set　that　is　outside.　Experimental　results　on　twelve　real-world　datasets　show　that　the　proposed　classifier　is　generally　better　than　the　other　two　piecewise　linear　classifiers.　Moreover,　a　comparison　with　several　types　of　support　vector　machines　confirms　its　competitiveness.　(C)　2019　Published　by　Elsevier　Inc.