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Four-coloring a Dodecahedron (github.com)
26 points by jnotarstefano 1640 days ago | hide | past | web | 22 comments | favorite

Sorry, the controls are insane. I move mouse out to rotate the figure to see the face I want to change color for, then I move mouse in and the dodecahedron rotates again, moving the desired face back. Please, add some arrow controls or something different from mouse movement to rotate.

Otherwise neat and hope you find a good internship.

That was fun - possibly the seed of a great video game :) .

Probably the easiest fix for the controls would be to limit which mouse movements move the shape: moving down would spin it up, but moving up would do nothing. Moving left would spin it right, but moving back across it would do nothing. That way you could move it into place and then come back to click on where you want.

Also, it would be lovely if the most centered face, the one that is changeable, became outlined when it comes into focus.

I agree: it's barely usable as it is. I hacked it this very night, and those were the best controls I was able to build. Thank you for playing and for the critique!

You might also want to cull backwards polygons or use a depth buffer.

It's an interesting idea. Perhaps use keyboard rotation controls?

Oh this is really cool, and one of the few demos I actually want to interact with. But alas I am unable to control it in any kind of intuitive way, thus it is useless (sorry) Fix the UI please!!!

EDIT: Oh and add a histogram of how far along a solution you are

The four-color theorem is typically formulated for planar figures. It also applies to the surface of anything homeomorphic to a sphere, because a stereographic projection will preserve the four-color property. It does not apply to other shapes -- a simple torus may need seven colors. Adding holes lets you increase the number of required colors without bound.

Is there a statement for polyhedra similar to four-color theorem?

I could only google a book called "Map Coloring Polyhedra and the Four Color Problem". Unfortunately, it's not available to read online. From what I've found, it seems to me that there is only a handful of proven facts about colorings of some polyhedra.

[ADD]: four color theorem works for every planar graph and it looks like one can make such graph corresponding to any convex polyhedron, so it seems that original OP statement holds.

Just make a hole in the center of one side of the polyhedra. Then stretch out the hole, flattening the polyhedra in the process. Eventually you get a planar map, while retaining the same topology as the original polyhedra.

Or, in math-speak, the polyhedron is homeomorphic to the sphere, and a stereographic projection of the sphere will preserve the four-color property while projecting the sphere to a plane.

I first thought, "That's exactly what I said," and then I realized that "homeomorphic" isn't exactly a household word.

"It's harder than it looks" is talking about the mouse controls, right?

On my 1366x768 laptop in chrome, the dodecahedron covers some text. I had to zoom out to read it.

Same here on 1280x800. Also some faces of the dodecahedron moves weirdly compared to the others (Firefox 17.0.1).

This is a very serious blunder on my part! That's an important resolution to support.

The same happens for me at 1440x900.

The problem is that your rotation is relative to the dodecahedron, not the page, and that it uses inverted vertical rotation but not horizontal so it's kind of hard to get used to IMO. I would also switch to movement when a user clicks and drags as opposed to whenever they move the mouse.

"It is harder than it looks" foremost because the usability of that coloring app needs improvement.

Fun! Best of luck finding your internship.

As for the control, here is what I would do:

    Imagine a circle on the center of the screen that stopps the spin, outside the circle, rotate with a speed proportional to the distance from the center.

I tried it and almost couldn't solve it because of the weird acceleration. If you are having this issue too, go into the dev console and change around the MS_BTW_UPD variable. I personally like MS_BTW_UP=18

MS_BTW_UPD (which stands for "Milliseconds between updates") was changed to 18. Thank you for your feedback!

Really interesting mathematics I hadn't heard about before! The controls feel a bit clunky, and clicking on a side doesn't change the color sometimes.

Great job, good to see people making stuff on here.

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