Tag Archives: hexagon

A Tessellation Using Tetraconcave Octagons, Convex Hexagons, and Concave Heptagons

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A Chiral Tessellation of Tetraconcave Octagons, Convex Hexagons, and Concave Heptagons

Dodecahedral Polyhedron Featuring Regular Icosagons, Regular Hexagons, Rectangles, and Isosceles Trapezoids

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Polyhedron Featuring Regular Icosagons, Regular Hexagons, Rectangles, and Isosceles Trapezoids

Created with Stella 4d, software you can try and/or buy at http://www.software3d.com/Stella.php.

Cube-Based Polyhedron Featuring Regular Icosagons, Regular Hexagons, and Isosceles Trapezoids

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Polyhedron Featuring Regular Icosagons, Regular Hexagons, and Isosceles Trapezoids

Created with software you can try and/or buy at http://www.software3d.com.Stella.php.

150 Irregular Hexagons, Rotating About a Common Axis

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150 Irregular Hexagons, Rotating About a Common Axis

There are sixty of the irregaular, pentagonal gaps. Also, the hexagons themselves are of three types, two of which are sixty in number, and one of which is thirty in number.

If the gaps are filled, and the color scheme changed to make each of the four polygon-types into its own color-group, this looks, instead, like this (click on it if you wish to see it enlarged). It has 210 faces.

60pentagons and 60and60and30hexagons total faces 210

(Images created with Stella 4d — software you can try yourself at http://www.software3d.com/Stella.php.)

Tessellation Using Regular Triacontakaihexagons, Equiangular Hexagons, Isosceles Triangles, and Isosceles Trapezoids

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Tessellation Using Regular Hexacontakaihexagons, Equiangulr Hexagons, Isosceles Triangles, and Isosceles Trapezoids
The equiangular hexagons are very nearly regular, with only tiny deviations — probably not visible here — “from equilateralness.”

Tessellation Using Regular Octadecagons and Triconcave, Equilateral Hexagons

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Tessellation Using Regular Octadecagons and Triconcave Equilateral Hexagons

Tessellation of Regular Dodecagons and Regular Enneagons, Together with “Bowtie” Hexagons

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A Polyhedron with 122 Faces

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A Polyhedron with 122 Faces

The 122 faces are twenty blue, irregular hexagons; thirty red, irregular hexagons; 60 rectangles, and twelve regular pentagons.

Software credit: just visit http://www.software3d.com.Stella.php, and look for the free trial download of Stella 4d, the program I used to make this rotating image.

Snowflake in Blue and Yellow

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Snowflake in Blue and Yellow

Twenty Hexagons with Heptagrammic Designs

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Twenty Hexagons with Heptagrammic Designs

The design on the hexagons appeared in the last post here, and was created using Geometer’s Sketchpad and MS-Paint. After that, I used another program, Stella 4d, to place these images on the hexagons of a truncated icosahedron, render the pentagons invisible, and create this rotating .gif file.

Stella 4d may be tried and/or purchased at http://www.software3d.com/stella.php.