I received a commission to make a highly unlikely dodecahedron, and after what seemed like a billion stitches, here it is.
A quick off-the-cuff estimate suggest that this piece contains around 3000 beads. It's roughly the size of a baseball. Ten different colors of beads
show the ten paths that twist and wrap around the surface. Each path encircles one of the ten axes of 3-fold rotation symmetry of the dodecahedron. (Those axes go through opposite vertices of the dodecahedron so that the paths are like belts that twist around the equators of those axes.)
If you want to learn more about how I discovered this shape, check out my blog post on
Highly Unlikely Triangles and Other Impossible Figures in Bead Weaving. There, you can find a link to download the paper I presented at the Bridges Conference in 2015.
I don't have a tutorial for the dodecahedron, but I do have a tutorial for a related and simpler design, the
Highly Unlikely Triangle, shown below with bugle beads, but you can also use just seed beads. Thanks for looking.
Beautiful!
ReplyDeleteI have another idea for you: Create the table of the elements as a net of beads where each sphere represents an element, and struts connect each with their immediate neighbors in both atomic number (row) and in their family (column). You can follow my diagram here: http://superliminal.com/pfractal.htm Use different colored balls for various element types. You only need 100 or so. Let me know if you have any questions.
Love these pieces. In addition to the mathematical/moebius strip aspects, the quarter twist would do so much to stiffen up the piece and help it hold its shape.
ReplyDeleteThank you Emilie. What you described is exactly what happened! Great insight! In fact, I think I could make the edges *at least* two units longer and have the whole thing remain stiff.
DeleteGreat stuff. Loved the polyhedra ( what former math student / board gamer doesn't?) Loved the bacteriophage. I remember reading about phages in a book on the discovery of DNA. Shared your work with others.
ReplyDeleteDid my comment get lost? Just in case, was saying I loved the polyhedra. Loved math in school, in spite of my poor arithmetic skills ( got a minor in math in college.) And played board games and games like D&D where you get to play with lovely numbered polyhedra. Shared your work with friends
ReplyDeleteThank you Michael! Certainly my enjoyment of board games as a kid fueled my love of polyhedra today.
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