Behold: A hole thru a hole in a hole

Hole hole hole
You'll tell your grandkids about the day you saw this. (Thanks Clifford Pickover!)


  1. Is there a name for this sort of construct?  It reminds me of a Klein Bottle, but I wonder if it’s a bit different enough that it has its own name…

      1. I think topologically it is a triple torus, arranged to be cool enough that I want to get a 3D printer and try it out.

        Compress it left-right a bit in your head and you can see the inner whole is just two holes. Stretch front-back and do a half-twist of the center and it looks just like the middle triple torus in the wikipedia article.

        1. No, the 3-torus is both 3-dimensional (while this is 2 dimensional) and not embedable in standard 3-space.  This is a genus 3 orientable surface.

          Edit: I just scrolled down the wikipedia page you linked to and saw that they both have the 3 torus and the genus 3 surface both listed as the “triple torus”. So you are correct. I have to say, as a topologist, wikipedia is the only place I have ever heard this terminology.

    1. What’s the difference between a tube and a hole? If you squashed that shape flat along one of its dimensions, wouldn’t the hole be unambiguously a hole? What if it were not quite flat but just a millimeter or so thick? If a worm eats through my shirt, hasn’t it just made a really short tube for itself?

      1. it’s kind of like obscenity. i can’t really define a hole, but I know it when i see it.

        ok, seriously? i don’t know the definition of a hole. but i guess in MY mind it’s a gap in a plane. a hole may be defined by a place where a gap in a plane starts a tube, but the hole itself is just the gap in the plane. but i have zero anything to back that up.

        1. A tube without a hole is not a tube. The tube contains the hole. A hole must allow for the passage of objects from one place to another, therefore, we can say that the tube is either:

          1. an enclosed space with two holes, both leading inside
          2. two holes joined by a tunnel
          3. a single hole running through the length of the object.

          Actually, I have no idea what that proves. Go ask Jeremy Hillary Ph.D. 

  2. I predict sometime in our lifetime we will have a hole through a hole through a hole in a hole. And as we approach the singularity, we will go deeper.

  3. Woo-head guest at party: Y’know (whispered in an awed voice) the Navaho have a really weird language. It’s *so* weird that they have a special word for the holey bit inside a tube.

    Me: Of course, so does English. Bore. 

  4. Am I the only one who just see the hole thru the hole but not the hole they’re in ? Unless I see the hole in the hole (so these two holes) but not the one to go thru…

  5. “…any whole hole with a hole bitten in it
    Is a holey whole hole,
    And it Just… Plain… ISN’T!”

    (From a doughnut song in Homer Price, as recalled)

Comments are closed.