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An entry in Fortnightly Topic Challenge #33: Surface Geometry Mazes

Behold, a tricky maze created on the surface of a cube. There are 'nodes' to collect and tunnels to traverse, are you up to the challenge?

Cube

I have unfolded the cube and created a legend to aid your mission, you can also find the rules below! (Click images for a closer look):

RulesAndLegend

Here is the maze in all it's unfolded glory, remember even in this condition it is still a cube!:

MazeUnfolded

Answers should adhere to the above parameters, shown preferably with a nice long scrawl over my original image but feel free to improvise!

There is at least one correct path but as with the nature of such a puzzle other solutions may exist. The first answer given that meets the criteria will be awarded the tick, if it's quite different to my solution I will also share mine as a second answer :)

Extra information for those that like to think out of the box, you can't jump walls, climb, fly, reach that node just over there, squeeze past your old paths, re-use tunnels or become a giant to take the whole maze and all it's nodes in one grab, etc ;)

EDIT: Quick rules clarification as a relative brought it up when attempting the puzzles, use of tunnels is optional. Whether completion is possible without them is another thing!

Good luck and I hope you have fun solving it!

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    $\begingroup$ Few we didn't only have one question at the end of the fortnight (and here is 1k, grats! :) ) $\endgroup$
    – Beastly Gerbil
    Commented Jul 14, 2017 at 15:05
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    $\begingroup$ And I just realised I can't spell 'phew' $\endgroup$
    – Beastly Gerbil
    Commented Jul 14, 2017 at 15:33
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    $\begingroup$ Very stylish puzzle! Really nice looking. I like your tunnel innovation on the classic maze. $\endgroup$
    – Forklift
    Commented Jul 14, 2017 at 15:49
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    $\begingroup$ I will make a 3D Printable version of the cube maze available (with and without nodes) for anyone that would like a .stl, let me know and I'll upload to Thingiverse. $\endgroup$
    – BreakingMyself
    Commented Jul 14, 2017 at 15:50
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    $\begingroup$ I hope we aren't being chased by ghosts while doing this. $\endgroup$
    – Gareth McCaughan ♦
    Commented Jul 14, 2017 at 15:55

2 Answers 2

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This seems to work:

enter image description here

Green is the path. Purple is showing how many times we enter each face.

Highly sophisticated method of solution: Trial and error. (I started by filling in things that were forced, then just drew stuff. I ended up with a couple of loops and some bits that wouldn't connect, and fixed things up incrementally.)

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  • $\begingroup$ Wow awesome, some sections are just like mine but your overall route is different, quick work well done! :) $\endgroup$
    – BreakingMyself
    Commented Jul 14, 2017 at 16:33
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As promised, here is my solution that was made when designing the maze:

Path

I will probably make another in the near future as it was a fun process. For those wondering I used Fusion360 to make the maze and Clip Studio Paint for the additional details.

For the next maze I would like some suggestions and feedback if possible so please comment below or ping me on the chat.

A bigger cube?
A different shape?
Better layout/decorative details?
Bridges (maybe between multiple shapes)?
More restrictions/rules?
Non-Euclidean shapes?
Don't bother? ;)

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    $\begingroup$ I like the bridges idea and also maybe a door/key combo where you need one before taking that path? Perhaps one way paths? $\endgroup$
    – Forklift
    Commented Jul 17, 2017 at 19:43
  • $\begingroup$ Fantastic ideas. If I use either I will be sure to credit you :) $\endgroup$
    – BreakingMyself
    Commented Jul 17, 2017 at 21:06

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