Camping In Hexagonal Tents On a Tessellated Plane

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Camping In Hexagonal Tents On a Tessellated Plane

Squares and Triangles

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Squares and Triangles

Here’s what it looks like with different colors (click to enlarge it):

tess with sq & tri 2

A Gallery of Nine Tessellations Using Hexagons

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hextess

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.

Hex radial tessellationHex radial tessellation 2Hex radial tessellation 3Hex radial tessellation 4radial octagonal mandala 2radial octagonal mandala 2Buntitleduntitled ic

A Rhombic Dodecahedron Featuring Rotating Pentagonal Mandalas

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A Rhombic Dodecahedron Featuring Rotating Pentagonal Mandalas

Geometer’s Sketchpad and MS-Paint were both used to make the images on the faces of this polyhedron, and then Stella 4d was used to put it all together and create this rotating image. Stella may be bought, and/or tried for free, at www.software3d.com/Stella.php.

A Pentagonal Mandala In Primary Colors

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A Pentagonal Mandala In Primary Colors

A Chiral Tessellation

A Chiral Tessellation

In this chiral tessellation, the blue triangles and green hexagons are regular. The yellow hexagons are “Golden Hexagons,” which are what you get if you reflect a regular pentagon over one of its own diagonals, then unify the two reflections. The pink and purple quadrilaterals are two types of rhombi, and the red hexagons are a third type of equilateral hexagon. All of the edges of all polygons here have the same length.

There are three different types of points of three-fold rotational symmetry repeated here. Two of these types are centered in the middle of blue triangles, while the third is centered in the middle of some of the green hexagons — specifically, the ones surrounded only by alternating red and yellow hexagons.

When I try to generate the mirror-image of this tessellation, it overloads Geometer’s Sketchpad, and crashes the program. However, inverting the colors of the same reflection, in MS-Paint, to make a color-variant, is easy:

weird tessellation

Tessellation Using Equilateral Triangles, Isosceles Triangles, Squares, Regular Pentagons, and Equilateral, Non-Convex Octakaitetracontagons

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In this tessellation, regular polygons have been given the brighter colors, while the two non-regular polygons have pastel colors.

Tessellation of the Plane with Regular Hexagons, Squares, and Tetraconcave, Equilateral Octagons, #1

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Tessellation of the Plane with Regular Hexagons, Squares, and Tetraconcave, Equilateral Octagons

If you’d like to see the second version of this tessellation, made over a decade later, simply click right here.

Black Widow

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Black Widow

Tessellation Using {8/3} Star Octagons and Squares

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Tessellation Using {8/3} Star Octagons and Squares

The tessellation of the plane which uses regular convex octagons and squares is well-known. This related tessellation, however, is not. I didn’t know it existed until I stumbled across it . . . although I very much doubt I am the first person to do so.