# Vertex figures and tessellations

Another definition of a regular tessellation is one whose vertex figures are identical regular polygons.

A vertex figure is made by connecting the midpoints of all the edges which touch a given vertex.

(1) Sketch the vertex figures for the regular semiregular tessellation of the plane and verify the definition.

(2) The dual of the tessellation is a new tessellation formed by connecting the centers (centroids) of polygons that share a common side. Find the duals of the regular tessellation.

(3) Common notation for describing regular or semiregular tessellations uses vertex arrangements, which list the number of sides of each polygon going around the vertex. Give the vertex arrangements for the regular and semiregular tessellations.

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#### Solution Summary

This provides information about vertex figures and tessellations, including verifying definitions, duals of a tessellation, and notation.