A Tessellation Featuring Regular Heptagons

Tessellation Featuring Regular Heptagons

Regular heptagons, of course, can’t tile a plane by themselves. Of all tessellations of the plane which include regular heptagons, I think this is the one which minimizes between-heptagon gap-size (the parts of the plane outside any heptagon). However, I do not have a proof of this. The shape of each of the polygons which fill the “heptagon-only gaps” is a biconcave, equilateral octagon. With these octagons, this is a tessellation, but without them, it wouldn’t fit the definition of that term.

[Later edit:  on Facebook, a friend showed me two others with smaller gap-sizes. In other words, the conjecture above has now been shown to be wrong.]

About RobertLovesPi

I go by RobertLovesPi on-line, and am interested in many things, a large portion of which 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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5 Responses to A Tessellation Featuring Regular Heptagons

  1. Anonymous says:

    Very interesting but not good enough.


  2. alexbateman says:

    Can you provide links to the other heptagon tilings with smaller gaps?

    Liked by 1 person

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