Tag Archives: polygon

Zonohedra, Zonish Polyhedra, and Another Puzzle

In a recent post, I showed many images of zonohedra, then challenged readers to figure out, from the images, what zonohedra are: polyhedra with only zonogons as faces. Zonogons, I then explained, are polygons with (A) even numbers of edges, … Continue reading

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Octagons Can Tile a Plane II

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 … Continue reading

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Two Colorings of a Tessellation Featuring Regular Polygons with 24 Sides

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The Second of Dave Smith’s “Bowtie” Polyhedral Discoveries, and Related Polyhedra

Dave Smith discovered the polyhedron in the last post here, shown below, with the faces hidden, to reveal how the edges appear on the back side of the figure, as it rotates. (Other views of it may be found here.) … Continue reading

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On the Possible Numbers of Vertices of Extended Convex Polygons

A few days ago, I came across the phrase, while surfing the Internet, “the extended quadrilateral has six vertices.” Not understanding this, I researched the matter, and found out what this phrase means. If the normal four vertices of a … Continue reading

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An Icosagon, with Its Diagonals

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Polygons Related to the Golden Ratio, and Associated Figures in Geometry, Part 2: Quadrilaterals

The golden ratio, also known as φ, has a value of [1 + sqrt(5)]/2, or ~1.61803. It is associated with a great many figures in geometry, and also appears in numerous other contexts. The most well-known relationship between a geometric figure … Continue reading

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