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