Octagons Can Tile a Plane II

Posted on 2 January 2016 by RobertLovesPi

In April 2014, I found a tessellation of the plane which uses two kinds of octagons — both types equilateral, but only one type regular.

Now, I have found two more ways to tessellate a plane with octagons, and these octagons are also equilateral. However, in these new tessellations, only one type of octagon is used. One of them appears below, twice (the second time is with reversed colors), and the other one appears, once, in the next post.

tessoct

tessoct 2

Five Versions of a Tessellation Using Squares and Equilateral Triangles

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Tessellation Using Squares and Triangles

I used four other color-schemes with this same tessellation, and those other images are shown below.

A Gallery of Nine Tessellations Using Hexagons

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Pictured above is the most familiar hexagonal tessellation. I’ve found some additional tessellations which use equilateral (but non-equiangular) hexagons, and have radial symmetry. They appear, using various coloring-schemes, below.