In geometry, a truncation is an operation in any dimension that cuts polytope vertices, creating a new facet in place of each vertex.

We start with a polygon — let's say a triangle. This triangle has 3 vertices. In order to truncate we need to split each vertex into two. Now the triangle is made up of 6 vertices. Or rather 3 pairs of vertices. Each pair occupies the same position as the original vertex it is split from.

The vertices are used to define the sides of a triangle. Therefore, each vertex has a direct *relation* to a side. The process of truncation involves moving each vertex along it's line towards the mid-point of the line.

Once all the vertices reach the mid-points this is known as **Complete Truncation**. If we keep moving beyond the mid-point then it is known as **Hypertruncation**. As we execute Hypertruncation there is a point where the vertex reaches the starting location of the vertex directly opposite to itself. If we keep going beyond that location then we are executing **Quasitruncation**. Lastly, we can also go away from the mid-points. This is known as **Antitruncation**.