# \#tesselation

**URL:** https://scanalyst.fourmilab.ch/tag/tesselation/411.md

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## [π = 4? π = ∞? The Puzzle of the Schwarz Lantern](https://scanalyst.fourmilab.ch/t/4-the-puzzle-of-the-schwarz-lantern/4152)

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**Author:** [@johnwalker](https://scanalyst.fourmilab.ch/u/johnwalker)\
**Replies:** 0\
**Last updated:** [29 December 2023 14:52 UTC](https://scanalyst.fourmilab.ch/t/4-the-puzzle-of-the-schwarz-lantern/4152 "2023-12-29T14:52:19Z")

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Here is more about the Schwarz lantern. The pathological behaviour it illustrates when approximating smooth curved surfaces with a triangular mesh is all too familiar to those working with automatically-ge…

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## [An Aperiodic Monotile](https://scanalyst.fourmilab.ch/t/an-aperiodic-monotile/2926)

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**Author:** [@johnwalker](https://scanalyst.fourmilab.ch/u/johnwalker)\
**Replies:** 1\
**Last updated:** [22 March 2023 19:00 UTC](https://scanalyst.fourmilab.ch/t/an-aperiodic-monotile/2926 "2023-03-22T19:00:18Z")

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In a paper posted on arXiv on 2023-03-20, “An aperiodic monotile”, four authors report discovery of a polygonal shape that tiles the plane but never repeats in arbitrarily large patches. This is called an “aperiodic til…

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## [News You Can Use: Regular Heptagons Tile the Hyperbolic Plane](https://scanalyst.fourmilab.ch/t/news-you-can-use-regular-heptagons-tile-the-hyperbolic-plane/961)

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**Author:** [@johnwalker](https://scanalyst.fourmilab.ch/u/johnwalker)\
**Replies:** 0\
**Last updated:** [2 March 2022 15:05 UTC](https://scanalyst.fourmilab.ch/t/news-you-can-use-regular-heptagons-tile-the-hyperbolic-plane/961 "2022-03-02T15:05:15Z")

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At the same time, the regular heptagon is the smallest regular polygon which cannot be constructed with a ruler and straightedge. This is because 7 is a Pierpont prime but not a Fermat prime.

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## [2–4–6–8, All Quadrilaterals Tesselate!](https://scanalyst.fourmilab.ch/t/2-4-6-8-all-quadrilaterals-tesselate/353)

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**Author:** [@johnwalker](https://scanalyst.fourmilab.ch/u/johnwalker)\
**Replies:** 0\
**Last updated:** [12 November 2021 13:16 UTC](https://scanalyst.fourmilab.ch/t/2-4-6-8-all-quadrilaterals-tesselate/353 "2021-11-12T13:16:34Z")

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More formally, Any triangle or quadrilateral (even non-convex) can be used as a prototile to form a monohedral tessellation, often in more than one way. Copies of an arbitrary quadrilateral can form a tes…