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

[Peter Dow]

I'm going to try for the "Mathematics" forum for this topic but no worries if the mods decide to move this to "The Lounge".

 

I've posted this image which I've described as a
"Three-spoke dovetailing tile tessellation".

 

Trispokedovetile tessellation by Peter Dow, on Flickr

 

which is a tessellation of this tile shape,

 

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.

[Sriman Dutta]

Interesting shape...

[Peter Dow]

Trispokedovetiles Animation Webpage

 

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.

 

A still image from the animation is attached - showing trispokedovetiles with "CIRCLE" = 125%.

 

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.

Edited November 19, 2016 by Peter Dow

[Peter Dow]

Tutorial on how to produce 3D images from my trispokedovetiles webpage

 

A trispokedovetile in 3D

 

3 trispokedovetiles in 3D

[Peter Dow]

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%.

 

 

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 attaching 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.

 

 

Stacking and joining those together forms a bilayer trispokedovetile, "C100+C121".

 

 

Drawing the 2 layers semi-transparently we can see how the bilayer trispokedovetiles would interlock in the normal to the plane.

 

 

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.

Edited November 29, 2016 by Peter Dow

[Trurl]

Very interesting. The question to answer is how it differs from a regular gear. Inter-locking the forces on the gear could be distributed differently. I am not sure of the inter-locking would allow circular motion. They would be in conflict during rotation.

 

However don't be deterred. If certain Pokadoves were stationary while others rotated as a gear you could produce custom orbits. That is irregular non-circulat orbits. Think unsemetric objects like a space station.

 

This is good work. I'm just giving my opinion. I am no authority on the subject. But you need to research gears in a machine design book. Again cool shape; creative design; I'm just not sure how it moves. Are you suggesting to use it as a mag wheel? Or is it to inter-lock as a tool?

[Peter Dow]

Very interesting. The question to answer is how it differs from a regular gear. Inter-locking the forces on the gear could be distributed differently. I am not sure of the inter-locking would allow circular motion. They would be in conflict during rotation.

 

However don't be deterred. If certain Pokadoves were stationary while others rotated as a gear you could produce custom orbits. That is irregular non-circulat orbits. Think unsemetric objects like a space station.

 

This is good work. I'm just giving my opinion. I am no authority on the subject. But you need to research gears in a machine design book. Again cool shape; creative design; I'm just not sure how it moves.

There's no "circular motion" nor "rotation" nor "wheel" movement intended.

 

Think jigsaw puzzle pieces

 

 

or interlocking paving tiles

 

 

to remember that not all things which interlock are intended to rotate.

 

I presume I have confused you with ...

 

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

 

 

However, the similar shape is where the similarity begins and ends between a 3-spoke wheel and a trispokedovetile, which is a TILE not a "wheel" nor a "gear".

 

Are you suggesting to use it as a mag wheel? Or is it to inter-lock as a tool?

I'm suggesting to use the shape for tiled armour -

 

Hexagonal ceramic armour tiles

 

- but tiled armour which interlocks.

Edited December 1, 2016 by Peter Dow

[Peter Dow]

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

 

- which generates Computer Numerical Control (CNC) code which I've tested with CNC Simulator Pro but not on a real CNC cutter as yet.

[Peter Dow]

HOLES!

Now cut trispokedovetiles by CNC laser cutter with (or without) HOLES!

 

 

[Peter Dow]

TRISPOKEDOVETILES ROUTER CUTTING
My trispokedovetile CAD-CAM webpage now offers an (X,Y,Z) option for router cutting using rotary tool paths between spaced out tiles -

I've simulated the CNC router code -

[tar]

If they interlock, shouldn't the shape cut out of an innie be exactly the same as the shape cut out around the outie? In other words, the pattern for cutting the tiles should have no waste. And the manufacture of this shape tile would be more readily done molding one tile at time from concrete, than cutting from a slab of stone of a certain thickness.

or are you using a jigsaw and having to account for the thickness of the blade?

sorry, you said that

 

it is a router path you are showing

nice tiles

[Peter Dow]

If they interlock, shouldn't the shape cut out of an innie be exactly the same as the shape cut out around the outie? In other words, the pattern for cutting the tiles should have no waste. And the manufacture of this shape tile would be more readily done molding one tile at time from concrete, than cutting from a slab of stone of a certain thickness.

or are you using a jigsaw and having to account for the thickness of the blade?

sorry, you said that

 

it is a router path you are showing

nice tiles

 

Thanks for expressing an interest tar.

 

"If they interlock, shouldn't the shape cut out of an innie be exactly the same as the shape cut out around the outie? In other words, the pattern for cutting the tiles should have no waste."

 

I don't follow you and don't want to invest the time to interrogate you to find out what you mean. It seems to be a unhelpful time-wasting conversational point in passing while you have no actual intention to cut any tiles yourself so I think I will pass on attempting to answer that one, sorry.

 

I don't wish to brush all enquires off but I don't wish to give the impression that I welcome any opportunity to engage in idle chit-chat because I don't.

 

However, if I have misunderstood and you or someone else has your own CNC cutter and really want to know how to cut some of these tiles then I would like to help that sort of genuine enquiry.

 

"And the manufacture of this shape tile would be more readily done molding one tile at time from concrete, than cutting from a slab of stone of a certain thickness."

 

A CNC cutter using my code could also be used to make a mould to make trispokedovetiles.

 

"or are you using a jigsaw and having to account for the thickness of the blade?

sorry, you said that

it is a router path you are showing"

 

Well the webpage offers 2 options according to whether you tick the "spaced" box or not

 

1. "spaced" unticked - cut tiles as assembled, assuming the kerf is narrow enough, as would be suitable for laser, plasma or water jet cuttting

 

2. "spaced" ticked - cut tiles separated, assuming a wider kerf, as would be suitable for router cutting

 

"nice tiles"

Thank you tar.

 

I've now added a Trispokedovetiles Gallery webpage because I've got some real tiles cut now.

 

 

 

[Peter Dow]

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.

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.

Edited July 1, 2017 by Peter Dow