A semi-regular tessellation is one consisting of regular polygons of the same length of side, with the same ‘behaviour’ at each vertex. An example of a semi-regular tessellation is that with triangle–triangle–square–triangle–square in cyclic order, at each vertex.

When we cover a surface with a pattern of a flat geometric shapes such that there should have no overlaps or gaps, then the surface is called a tessellation.

A regular tessellation is a design covering the plane made using 1 type of regular polygons. A semi-regular tessellation is made using 2 or more types of regular polygons. With both regular and semi-regular tessellations, the arrangement of polygons around every vertex point must be identical.

Tessellations

• RULE #1: The tessellation must tile a floor (that goes on forever) with no overlapping or gaps.
• RULE #2: The tiles must be regular polygons – and all the same.
• RULE #3: Each vertex must look the same.

The reason there are only eight semi-regular tessellations has to do with the angle measures of various regular polygons.

eight semi

However, there are only three types of regular polygons that can be used to form regular tessellations: triangles, squares, and hexagons. A semi-regular tessellation is made up of regular polygons as well, but instead of using just one repeated polygon it uses two or more of them to form a more complex pattern.

Regular tessellations of the plane by two or more convex regular polygons such that the same polygons in the same order surround each polygon vertex are called semiregular tessellations, or sometimes Archimedean tessellations.