I'm going to try for the "Physics & Math" forum for this topic but no worries if the mods decide to move this to "Art & Culture" or "Architecture & Engineering". I've posted this image which I've described as a "Three-spoke dovetailing tile tessellation". Please Register or Log in to view the hidden image! Trispokedovetile tessellation by Peter Dow, on Flickr which is a tessellation of this tile shape, Please Register or Log in to view the hidden image! Trispokedovetile by Peter Dow, on Flickr Check my Flickr page for the preceding design iterations and inspiration. I've named the shape Trispokedovetile which is a contraction of "tri-spoke dovetailing tile". "tri-spoke" because the shape is similar to a 3-spoke motorcycle wheel with three bites taken out of it. "dovetailing" because the tiles interlock like a dovetail joint But it is quite possible this shape is already known to geometry and already has been named. Do you know if this shape has already been named? If so please do reply to tell me what the name is.
It's a triangle grid based tessellation, there are literally an infinite number of shapes one could make. Cool though. I'm reading a book entitled "Escher on Escher", where he details his methods. Pretty amazing considering he didn't even have a computer.
But I've circled the triangle, too. Well it was inspired by geometric art by Jay Friedenberg [link] but is my "trispokedovetile" shape just more cool art, or could there be engineering applications, such as armour tiles [link], on account of the dovetailed joint between tiles? Well I should credit my computer javascript programming that helped me to produce this design.
Well what did you have in mind? Meanwhile, I've been busy in 2 dimensions ... Trispokedovetiles Animation Webpage [LINK] I've programmed a webpage using Javascript to display an animation which shows a range of different trispokedovetiles, each of which can be specified by a "CIRCLE" percentage, which is the ratio as a percent of two parameters - 1. A "HEXAGON" parameter length - always nominally "100%" 2. A "CIRCLE" parameter length - the animation varies this between 100% and 135%, though up to 150% is possible in theory. So you can specify the "CIRCLE" percentage to specify a particular shape of trispokedovetile. Here is a still image from the animation - showing the trispokedovetiles with "CIRCLE" = 125%. Please Register or Log in to view the hidden image! I've tested the animation in Chrome and Internet Explorer browsers and it works fine for me. But it is not working in Firefox for some as yet unknown reason. Let me know by replying here if you have any other problems with the animation not displaying for you.
Tutorial [LINK] on how to produce 3D images from my trispokedovetiles webpage [LINK] Please Register or Log in to view the hidden image! A trispokedovetile in 3D Please Register or Log in to view the hidden image! 3 trispokedovetiles in 3D
Now to consider the important issue of interlocking trispokedovetiles against movement in the direction normal to the tiled plane, which for the application of tiled armour would be the normal to the armour surface, in the direction of a bullet's path. BILAYER TRISPOKEDOVETILES I propose that the unit armour tile be comprised of 2 joined trispokedovetiles with matching HEXAGON parameters but each with a different CIRCLE percentage. For example, suppose we choose trispokedovetiles with CIRCLE = 100% and 121%. Please Register or Log in to view the hidden image! Please Register or Log in to view the hidden image! The reason for choosing C100 for the outer layer of the armour is because its 120 angle corners would be more robust. The reason for choosing C121 for the inner layer of the armour is because CIRCLE = 121% offers the largest percentage where the neck attacking the outer part rings is at least twice the thickness of the ring, attempting to balance the robustness of the ring parts to the robustness of the neck versus tensile stresses. Please Register or Log in to view the hidden image! Stacking and joining those together forms a bilayer trispokedovetile, "C100+C121". Please Register or Log in to view the hidden image! Please Register or Log in to view the hidden image! Drawing the 2 layers semi-transparently we can see how the bilayer trispokedovetiles would interlock in the normal to the plane. Please Register or Log in to view the hidden image! 2/3rds of the tiles can be slotted together, either the yellows and the blues or the yellows and the purples or the blues and the purples. However the final 1/3rd of the tiles would not simply slot in and would have be inserted by joining the two halves of the bilayer trispokedovetile in situ.
Typos - "its 120 degree angle corners" "the neck attaching the outer part rings" "would have to be inserted by joining"
For Computer-Aided Manufacturing of trispokedovetiles, I'm publishing today my new Javascript web-page - Trispokedovetiles: CNC code to cut tiles web-page G-code generator [LINK] - which generates Computer Numerical Control (CNC) code which I've tested with CNC Simulator Pro [LINK] but not on a real CNC cutter as yet.
HOLES! Now cut trispokedovetiles by CNC laser cutter with (or without) HOLES! [LINK] Please Register or Log in to view the hidden image!
Indeed. The regular hexagon shapes are only partly drawn (see diagram) and the hexagon edges do not correspond to the edges of single tiles, but I find the term "HEXAGON" useful for a parameter length for trispokedovetiles, referring to the length of the maximal diameter of the partly drawn regular hexagons. Please Register or Log in to view the hidden image!
TRISPOKEDOVETILES ROUTER CUTTING (LINK) My trispokedovetile CAD-CAM webpage now offers an (X,Y,Z) option for router cutting using rotary tool paths between spaced out tiles - Please Register or Log in to view the hidden image! I've simulated the CNC router code - Please Register or Log in to view the hidden image!
Quite similar: http://www.tessellation.info/en/info/artists/26/d/406/Three_Arrows The shapes have wallpaper group p6m symmetry, but with colors, this is p3m1 symmetry. https://en.wikipedia.org/wiki/Wallpaper_group#Group_p3m1_.28.2A333.29
I've collected a number of similar images on my "three-head arrows" board on pinterest. [LINK] Er, thanks. Please Register or Log in to view the hidden image! Oh I nearly forgot - I've now added a Trispokedovetiles Gallery page [LINK] because I've got some real tiles cut now. Please Register or Log in to view the hidden image! Please Register or Log in to view the hidden image! Please Register or Log in to view the hidden image!
BEWARE BAD LINKS ABOVE! I lost my website hosting in January. I was not "hacked" but the gcehosting administrator seems to have gone out of business and the hosting company he was using (godaddy) is serving various spurious adverts whenever anyone clicks one of my old links. I have got the following pages back on-line with a different hosting company now so try these links. Please Register or Log in to view the hidden image! LINKS Trispokedovetiles: Three-spoke dovetailing tiles by Peter Dow Trispokedovetiles: CNC code to cut tiles by Peter Dow Trispokedovetiles Gallery I can't edit my earlier posts to correct the old links, sorry. I've not done anything with this project since January.
