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Blender addon to create empties at verts, edges, and/or faces. See demo video

Available in the menu Object>Instancing++ or by operator search.

Verts

Empty is placed at the vertex with its +Z along the vertex normal. Other two axes are arbitrary

Edges

Only edges which join two faces are currently processed. A warning will be issued on how many edges are skipped.

Empty is placed at the midpoint with its +Z halfway between the face normals of its two adjacent faces. X is along the edge (sign is arbitrary). Y is arbitrary.

Faces

Empty is placed at the median center with its +Z along the face normal. X is along one of the faces edge (which edge and its sign are arbitrary). Y is arbitrary.