Geometry. Three-spoke dovetailing tile tessellation. "Trispokedovetile"?

Discussion in 'Physics & Math' started by Peter Dow, Nov 18, 2016.

  1. Peter Dow Registered Senior Member

    Messages:
    123
    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.
     

    Attached Files:

    Last edited: Nov 18, 2016
  2. Google AdSense Guest Advertisement



    to hide all adverts.
  3. spidergoat Speak of the Devil Valued Senior Member

    Messages:
    51,222
    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.
     
  4. Google AdSense Guest Advertisement



    to hide all adverts.
  5. Peter Dow Registered Senior Member

    Messages:
    123
    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.
     
  6. Google AdSense Guest Advertisement



    to hide all adverts.
  7. spidergoat Speak of the Devil Valued Senior Member

    Messages:
    51,222
    We need to make a 3D version, and see if we can create interlocking armor.
     
  8. Peter Dow Registered Senior Member

    Messages:
    123
    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.
     
  9. spidergoat Speak of the Devil Valued Senior Member

    Messages:
    51,222
    Very nice!
     
    Peter Dow likes this.
  10. Peter Dow Registered Senior Member

    Messages:
    123
    Last edited: Nov 23, 2016
  11. Peter Dow Registered Senior Member

    Messages:
    123
    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.
     
  12. Peter Dow Registered Senior Member

    Messages:
    123
    Typos -

    "its 120 degree angle corners"
    "the neck attaching the outer part rings"
    "would have to be inserted by joining"
     
  13. Peter Dow Registered Senior Member

    Messages:
    123
  14. Peter Dow Registered Senior Member

    Messages:
    123
  15. arfa brane call me arf Valued Senior Member

    Messages:
    5,163
    Apart from the dovetailing, your tiles have six sides but are not regular hexagons.
     
  16. Peter Dow Registered Senior Member

    Messages:
    123
    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!

     
  17. Peter Dow Registered Senior Member

    Messages:
    123
  18. rpenner Fully Wired Staff Member

    Messages:
    4,832
  19. Peter Dow Registered Senior Member

    Messages:
    123
    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!

     

Share This Page