This is a nylon model of a twisted torus
made by assembling identical units. It is a "speculative
reconstruction" of the historical artifact below, a twisted torus in
, assembled in the 16th century from seventy-six
The wood artifact above fits in the same
tradition of celebrating geometry as the following 1567 woodcut by the
German graphic artist Johannes
. This is the earliest printed image I know of a
My rapid prototyping model of the twisted torus is based on units of
the following shape:
Three units assemble at 90 degrees to
make the module below. Note that the unfilled slot is parallel to the
base plane of the rightmost wedge. So one can make an arbitrarily long
straight chain of these modules.
If the number of units is a multiple of
three, the modules can be curved around to close into a cycle with no
twist. Below is a no-twist cycle with 75 units (25 modules).
If the number of units is one more than
a multiple of three, it is natural to give it a slight twist before
closing. Below is an assemblage of 76 units. This is the same
number, twisted in the same manner, as the wood artifact above:
Below is an image of an analogous
construction with 77 units. It has the reverse twist from the above.
, in the Art History department at Indiana University, has
studied this object to understand its possible purpose. Bret told me
about this object and I made the computer models to get a sense of how
much play was needed in the slot in order to close the loop with a
twist but not so much play that it would feel sloppy and loose. He
made a walnut reconstruction of the units, shown below just before
closing the cycle.
Below is the closed loop after Bret was finished. Can you figure out
how to make the final connection?
My stl version is below. I didn't
make enough units to close the
loop, so I can only make an arc. Playing with these parts gives you a
hands-on opportunity to think about why this was made and how the loop
was closed. Was it a mechanical puzzle challenging the user to
disassemble it and reassemble it? Was it just a visual puzzle,
challenging the viewer to think about how it was assembled? Was
it a "masterpiece" displayed to prove the skill of the creator?
Was it functional, perhaps a trivet or laurel to be worn on the head
like a mazzocchio
workshop, perhaps a wooden
furniture or carriage maker, which someone casually put together into a
chain? I have no knowledge about any of this. Let Bret and
me know if you find out anything illuminating about these questions.
If you have access to a 3D printer and
want to make your own version of
these models, here are the stl files. The first two are for
making individual parts that you can link together. The last
three files are closed cycles; each is a rigid model in which the
parts intersect their neighbors slightly.
Adam Mayer uploaded my stl file to thingiverse
Charles Pax made this complete ring.
Makerbot folks kindly gave it to me at the NY Maker Faire.
Coincidentally, this was just four days befopre I happened to be going
made one also.
Beer Yeast Storage Device??
Surprisingly, it seems that this design may be what is
known in Danish as a "Gærkrans", which was apparently used to
collect and store yeast between beer brews. Thank you to Bodil
G., commenting on a Boing-Boing
post of my MakeZine
, for suggesting this. Here are
some references: 1