Type 4 Pentagonal Tiile

Type 4 Pentagonal Tile
Lucas Newman
George Mason University - Math 401 - Mathematics Through 3D Printing
September 10, 2021


This tile is an example of an irregular pentagon that is capable of tessellating with itself and tiling the whole plane.

When a shape can "tile the whole plane", this means that many copies of the shape can be placed edge to edge alongside each other, and that in doing this a pattern is created which can be extended in all two dimensional directions indefinitely. Regular pentagons do NOT have this property - if you try to place them into a tessellation they crowd each other and leave small gaps in the pattern. In order for a pentagon to tile in this way it must be instead constructed so that the sides and angles are NOT all identical, but DO adhere to constraints that endow it with this property.

Tiling pentagons can be placed into categories according to the specific set of geometric constraints by which they abide. These constraints consist o