Order-Six Radial Tessellations of the Plane, Using Elongated and Equilateral Hexagons, Rendered with Different Coloring-Schemes

I explored radial tessellations of the plane, using only hexagons, in this earlier post. Order-three tessellations of this type are the familiar regular-hexagon tessellations of the plane. With higher-order all-hexagon radial tessellations, though, the hexagons must be elongated, although they can still remain equilateral, and all congruent, with bilateral symmetry. In that previous post, examples were shown of order 4, 5, and 8, in addition to the familiar order-3 regular-hexagon tessellation.

This left out order-6, of which I show many examples below. As it turns out, this particular radial tessellation lends itself particularly well to a variety of coloring-schemes. In the first picture, the construction-circles, -points, and -lines I used are shown; in the rest, they are hidden.

No upper limit exists to the order-number of these all-hexagon radial tessellations — although the larger that number gets, the thinner the hexagons become, relative to their edge length. At some point (which I expect would vary from person to person), as the order-number increases, the hexagons needed will become so thin that they will no longer be recognizable as hexagons.

frequency 6 radial tessellation of hexagons with construction lines

Next, with construction artifacts hidden, are some two-color designs I found.

frequency 6 radial tessellation of hexagons without construction lines 2-color

frequency 6 radial tessellation of hexagons without construction lines 2-color version two

Here are some which use three colors each:

frequency 6 radial tessellation of hexagons without construction lines 3-color version colored by another system

frequency 6 radial tessellation of hexagons without construction lines 3-color version two

frequency 6 radial tessellation of hexagons without construction lines 3-color

frequency 6 radial tessellation of hexagons without construction lines 3-color version colored by rings

I also found some four-color patterns with interesting symmetry:

frequency 6 radial tessellation of hexagons without construction lines

frequency 6 radial tessellation of hexagons without construction lines. four colors version 2png

Finally, here are some which each use six colors.

frequency 6 radial tessellation of hexagons without construction lines 6-color version two

frequency 6 radial tessellation of hexagons without construction lines 6-color version colored by another system

frequency 6 radial tessellation of hexagons without construction lines 6-color

About RobertLovesPi

I go by RobertLovesPi on-line, and am interested in many things. The majority of these things are geometrical. Welcome to my little slice of the Internet. The viewpoints and opinions expressed on this website are my own. They should not be confused with the views of my employer, nor any other organization, nor institution, of any kind.
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