Faces vs Facets in Geometry.

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Faces vs Facets in Geometry.

In: Mathematics

In most fields of math that I’m aware of, these words are used interchangeably. In 3-dimensional geometry they both mean a flat polygon which is (generally) part of a surface of flat polygons. Like one face of a cube, or a face of a pyramid. More generally in n-dimensional geometry, a ‘face’ or a ‘facet’ is an n-1 dimensional shape which is analogous to the same thing.

I think in some computer graphics software’s nomenclature, only triangles can be “facets”, whereas faces can be any flat polygon with any number of edges. But that isn’t considered an official math definition.

Sometimes “face” will be used more informally to talk about an approximately-flat part of an actually very bumpy and irregular surface, like a rock face on a mountainside. In that less-formal context, people will generally only say “facets” when they’re talking about smaller, flatter surfaces such as those on a cut gem or a shattered window, or a quartz or pyrite crystal, things like that.

Faces = Flat surface that forms the boundary. Think the like the faces of a Pyramid.

Facets = Flat Surface that connects two polygons but is NOT a face. Image the bottom of one of the pyramids connected to [this](https://upload.wikimedia.org/wikipedia/commons/6/6f/First_stellation_of_octahedron.png) shape.