Rambling, and a cube with holes in it

by math_explorer, Sep 29, 2014, 2:09 PM

Sigh. I don't know why I'm not finding time to actually finish a Real Math Post™. Senior year isn't actually all that exhausting. Unlike last year, there's no crazy AP Economics workload, and the US Gov* teacher turned out to be much more of a storyteller than anybody would have guessed from his legendary summer homework assignments. Of course, there are college apps* and lots of various extracurricular activities and other responsibilities, but it doesn't feel like those scattered things would add up to be more than last year. And I feel like I'm procrastinating less.†

Um, I guess I posted real math posts before pretty rarely too. Oh well.

So, once again for the streak, an idle mathematical fill-in-the-blank exercise for the bored: Imagine a 3x3x3 cube. Remove seven unit cubes, one from the center of each face and one from the center of the whole cube. Then, the resulting polycube is topologically equivalent to a ___-fold torus.

---

* To anybody who doesn't know yet: yes, I live in Taiwan but go to a bilingual high school with a largely U.S.-style curriculum. And I have a U.S. passport. Which also means, yes, I'm competing with some of you for coveted spots at colleges. Well, actually, among the AoPSers I'm somewhat familiar with and know the current educational status of, I don't know anybody graduating the same year as I am, but I'm sure some of you are out there. (No hard feelings? :) )

† Plugging HabitRPG here. It motivated me with my life alarmingly well. I have evidence it doesn't work for everybody as magically as it did for me, but if you're also wrestling with staying productive and getting stuff done, I think it's worth a shot.

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4 Comments

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hm I think some other 2015 seniors:
DiscipulusBonus
MrE
briantix
apolygonne

hm darn can't think of anymore.

oh wait yeah lol forgot about djmathman and yugrey

also apple.singer

is B-t a senior? and I think BOGTRO
This post has been edited 1 time. Last edited by EpicSkills32, Oct 1, 2014, 5:51 AM

by EpicSkills32, Sep 29, 2014, 5:49 PM

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hmm i'm a 2015 senior too

by djmathman, Sep 30, 2014, 2:03 AM

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I am currently a senior.

by yugrey, Sep 30, 2014, 2:15 AM

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This was interesting.
  • I actually own a Void Cube a Rubik's cube in the shape you describe.
  • This shape is also a level 1 Menger sponge, which many people have already studied.

So the topological genus is $5$.

by PythonNut, Sep 30, 2014, 6:05 PM

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