Faceting

Faceting is like giving a shape a haircut! Imagine you have a big, solid block, like a giant LEGO brick. Faceting is when you carefully slice off parts of the block.

But here's the cool trick: you don't add any new corners or points where you slice! It's like making a new shape from the old one, but keeping all the original corners exactly where they were. This makes the shape look different, sometimes with more flat sides, but it's still connected to the original shape.

Think about a pizza. You can cut it into slices, and each slice has a straight edge. Faceting is a bit like that, but for 3D shapes like cubes or pyramids.

When you facet a shape, you might cut along lines that go across the flat sides (face diagonals) or even through the middle of the shape (space diagonals). These cuts can create new edges, but they never add new corners. It's a clever way to change a shape's appearance without making it more complicated with extra points.

When you facet a 3D shape, something super neat happens. Each edge of the original shape now has two flat sides meeting at it! Imagine a cube.

After faceting, it might look like it has more faces, but it's still made from the same basic structure. It's like taking a simple drawing and adding shading to make it look more detailed. Faceting can create new shapes or even make a shape look like it's made of several shapes stuck together.

Faceting is like the opposite of 'stellation'. Stellating is like adding pointy bits to a shape, making it look spiky. Faceting is like tucking those points in or slicing them off.

If you have a shape and you 'stellate' it, its 'dual' shape can be 'faceted' in a similar way. It's like two different ways of changing shapes, but they are connected, like a puzzle where one piece fits perfectly into another.