# Extrusion (InstanceTopic, 3)

### From Higher Dimensions Database

**Extrusion** is the simplest operation which creates an *n*+1-dimensional shape from an *n*-dimensional shape. Extruding a shape causes a prism to be formed, of which the base is the original shape. The length of the new prism can be specified as an argument to the extrusion operation. If unspecified, a common default is to use the length of the largest cardinal side.

After the extrusion, the number of elements change similarly to going down a row in Pascal's triangle. Each count is doubled and then increased by the count one dimension below it (and a single cell of the shape's dimension is formed). For example, when extruding the cube (which has 8 vertices, 12 edges, 6 faces and of course 1 cell), a tesseract is formed, which will have 8*2 = 16 vertices, 12*2+8 = 32 edges, 6*2+12 = 24 faces, 1*2+6 cells and a single new teron.