Octagons, Hexagons, and Squares

octagons hexagons squares

Hexagons and Octagons

hexagons and octagons

A Tessellation Featuring Multicolored, Regular Tetracontagons, as Well as Tetraconcave, Black, and Equilateral Hexatriacontagons

40

A Radial Tessellation of Regular Decagons and Bowtie Hexagons

decagon and bowtie hexagons

This tiling-pattern could be continued indefinitely, while still maintaining its five-fold radial symmetry, giving it the overall appearance of a pentagon.

An Icosagon, with Its Diagonals

icosagon

Blue-on-Blue Dodecahedron

dodecah3

This uses enlarged spheres centered on the dodecahedron’s vertices, overlapping so that they obscure the edges. Also, the faces are rendered invisible. I created it using Stella 4d, available at http://www.software3d.com/Stella.php.

A Tessellation of Regular Octadecagons and Three Types of Hexagon

tiling B

Thirty Golden Rectangles, Rotating About a Common Axis

The third image in the last post is a faceting of the icosidodecahedron. In that faceting, the faces used are equilateral triangles, star pentagons, and golden rectangles. To make these two new images, starting with that particular faceting of the icosidodecahedron, I rendered its triangles and star pentagons invisible, leaving only the thirty golden rectangles. It’s shown twice below, simply because I wanted to show it using two different coloring-schemes.

30 GOLDEN RECTANGLES

30 GOLDEN RECTANGLES RAINBOW

I would not be able to create images like this without the use of my favorite computer program, Stella 4d, written by a friend of mine who lives in Australia. You can try this program yourself, as a free trial download, at http://www.software3d.com/Stella.php.

A Geometrical Tiling Featuring Regular Icosagons, Pentagons, and Squares; Equilateral Octagons; and Equilateral, Octaconcave Hexadecagons

tiling

The only reason I am calling this simply a geometrical tiling, rather than a tessellation, is that I want to recognize the regular icosagons (twenty-sided polygons) as part of the pattern — and the icosagons here overlap, violating the established rules for tessellations.

Hexagons and Circles

hex