Question

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Use the numbering system to classify the tessellation of a plane with regular hexagons.

Answer 1

A tessellation is a covering of the plane by a repeating pattern of identical shapes. The shapes in a tessellation must fit together perfectly, with no gaps or overlaps.

There are three main types of tessellations:

• Regular tessellations:
  These tessellations are made up of regular polygons. A regular polygon is a polygon with all sides of equal length and all angles of equal measure.
• Semiregular tessellations:
  These tessellations are made up of two or more different regular polygons.
• Irregular tessellations:
  These tessellations are made up of irregular polygons.

The numbering system for tessellations is a way of classifying tessellations based on the number of sides of the polygons that make up the tessellation. The numbers in the system refer to the number of sides of the polygons in a single row of the tessellation.

`\boxed{\tt For \:example}`, a tessellation made up of regular hexagons would be classified as a 6-6 tessellation. This is because the hexagons in a row of the tessellation have 6 sides.

Here are some examples of tessellations with regular hexagons:

• 6-6 tessellation: This is the most common type of tessellation with regular hexagons. It is made up of a single type of regular hexagon, and the hexagons in a row have 6 sides.
• 3-6 tessellation: This tessellation is made up of two types of regular hexagons, one with 3 sides and one with 6 sides. The hexagons in a row alternate between 3-sided and 6-sided hexagons.
• 2-6 tessellation:
  This tessellation is made up of three types of regular hexagons, one with 2 sides, one with 3 sides, and one with 6 sides. The hexagons in a row alternate between 2-sided, 3-sided, and 6-sided hexagons.