# Convex hull (InstanceTopic, 3)

### From Higher Dimensions Database

The **convex hull** of a shape is a shape with the same vertices but with all other hypercells altered in the following way (the convex hull of multiple shapes is that of their union), where *n* is the dimensionality of the shape:

- Create (
*n*-2)-simplices over every appropriate set of vertices in the shape - Shrink a (
*n*-1)-hypersurface over the shape, blocked by the simplices, until its hypervolume is a minimum. This is now the convex hull of the original shape.