On the wikipedia page for a regular icosahedron they show {face,edge,vertex} normal projections in addition to {face,edge,vertex} projections, see here.
For example, here is the face normal projection
My question is how are these defined?
2026-03-27 00:04:40.1774569880
What are {face,edge,vertex} normal projections of polyhedra?
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I wouldn't say that there is a strict definition of these terms in the sense they are being used in these pics in Wikipedia.
For sure, you have 3 different elements in the icosahedron, any face, any edge, any vertex. So it would be better to speak of vertex-first projection (providing a decagonal picture), an edge-first and a face-first projection, as being seen in the very table of Wikipedia in the row above.
The mentioned pictures then are obtained by keeping the same axial alignments as above, but placing this axis into the paper plane, i.e. considering according side views. But note, this provides an one-parametric degree of rotational freedom for the orientation of such an arrangement.
--- rk