#OCTAGON TESSELLATION SERIES#

The final hinged tessellation here is composed of dodecagons. In the picture of the tiling above you can draw rhombs and squares that have their corners at the centers of the rings of octagons. The octagons rotate, adding triangles to the squares and then collapsing into a single octagon. Thus here the centers of the rings of octagons are the corner points of an Ammann-Beenker tiling. Note that this is the same condition as for stars of eight rhombs in the Ammann-Beenker tiling. Clearly, a ring of eight octagons arises if the squares here shown with black sides form an eight pointed star. Then there are four lines crossing in one point (indicated in red) making the octagons. Further out, perpendicular crossings correspond to squares of the tiling. Origami Tessellation artwork of Christine Edison. They result in two squares and four rhombs making up a dissected octagon at the center of the ring of octagons. If you’re curious about tessellations, some of these tutorials might be helpful to you figure out how people make some of their designs July 9, 2006. Surrounded by the yellow line we find intersections of several lines. Decorate your laptops, water bottles, notebooks and windows. The crossings of lines at the red points give the octagons. Unique Octagon Tessellation stickers featuring millions of original designs created and sold by independent artists.

#OCTAGON TESSELLATION SERIES#

Not only do they not have angles, but you can clearly see that it is impossible to put a series of circles next to each other without a gap. Which shape Cannot be used to make a tessellation Circles or ovals, for example, cannot tessellate. The center of a ring of octagons is indicated in yellow. Are octagons good for tessellation No, a regular octagon cannot tessellate. Should be fun.Dual grid of the tiling made of two dual grids of the periodic tessellation. I have yet to understand the complexity of this task, as well as the jargon. In some instances the patterns are monohedral (using only one tile throughout) sometimes 2 different pentagons, sometimes three. Octagon and squares Dodecagon and triangles 1 There are also. This Wikipedia article “ Pentagonal Tiling” is a little more complex than the Quanta magazine exploring the dilemma with pentagons, and the place I go to understand my next challenge.īelow are my first dozen tessellations exploring the regular division of the plane using convex pentagons. The figure that is used to tile the plane is a tessellation element and may consist of one. An article in Quanta Magazine explains the pentagon dilemma quite well.Ī dozen or so contributors took about 100 years to figure it all out, and confirm it all using computers. She was part of the extensive list of people involved in the study of pentagonal tiling, in the past century. Can a pentagon and an equilateral triangle tessellate A shape will tessellate if its vertices can have a sum of 360. Hexagons have 6 sides, so you can fit hexagons. This is not an integer, so tessellation is impossible. No there is no combination of 135 and 60 that adds up to exactly 360. Yes one octagon and two triangles meet at each vertex. Like a few years! Hey, I like a challenge.Īnother spur in the past few months about pentagons, was an obituary notice for Marjorie Rice, a tessellation artist from the States. No other regular polygon can tessellate because of the angles of the corners of the polygons. Yes two octagons and one triangle meet at each vertex. I think it will be a long time to completion. I have finally found a bit of time to start a study and hopefully an understanding of pentagonal tiling. Escher type nested shapes – and will always be. I had seen intriguing examples of pentagonal tiles over the years, but I was still obsessed with M.C. But wait I thought, aren’t pentagons impossible to tile using the original seventeen symmetry groups? Or so I thought. Hussein posted a beautiful Islamic geometric design, displaying the use of pentagons. Another challenge showing up on my desk, compliments of Woodpecker Carving.

Octagon tessellation