What is Snub in Geometry?


I was trying to find out what “snub” meant in geometry after I saw it as an option in Blender, but nothing I found explained it in terms I could understand. All I know is that it’s an operation done to a polyhedron.

Also, would it be correct to refer to performing said operation as “snubbing”?

In: 3

In geometry, a snub refers to a specific type of operation applied to polyhedra (three-dimensional shapes with flat faces) to create new shapes.

In general it’s when a twist is applied (generally to the same-shaped faces already on the polyhedron), which causes other flat faces to become multiple triangles to make the resulting shape work in 3D.

https://en.wikipedia.org/wiki/Snub_(geometry) the third image down (the gif) shows it visually.

If you have a uniform polytope in which every face has an even number of edges, you can delete alternate vertices (so that a regular octagon becomes a square, for example) fill the gaps with new facets. This is the most familiar kind of snub polytope.

For the result to be uniform, the new edges must be of equal length. In a two-dimensional figure like the surface of a polyhedron or a tiling of the (Euclidean or hyperbolic) plane, this requires solving two equations in two variables, so it’s always possible. But in three dimensions you need to solve five equations in three variables, so most topological snubs cannot be made uniform.