Quick Answer:

One common pattern for an envelope is shown below, but other shapes also are used.

Complete Solution:

To cover a sheet of paper with many copies of the same shape so that there are no holes or overlaps, the copies have to fit together. A rhombus, with four sides of equal length, as pictured below in red will do this.

To create tabs for gluing an envelope together, many manufacturers cut notches in the edges of each pattern, as shown in the following diagram. This is the only waste paper in the design. The pattern is then folded in the directions indicated by the arrows.

Other patterns also are used, such as the one shown below, but these may waste slightly more paper.