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Icositetrahedron ornament — A Premium Download from Crè

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A Renaissance masterpiece inspires a paper Christmas tree ornament in the shape of an Icositetrahedron Ornament
(composed of 24 identical faces) for you can downoload, print, and assemble…

What do you get when you combine 24 trapezia and a Vivarini Nativity? The Icositetrahedron Christmas Ornament, of course!
There wasn't much more in our geometry class in Greece in terms of teaching aids than a few solids made of polished wood: a cube, a pyramid, a sphere.

But what we lacked in accessories, our teacher, Mr. Christides, more than made up by his gifted teaching. One moment, we were contemplating Eratosthenes looking doing a well in Siene, Egypt—and figuring out the circumference of the earth!

Tthe next, we imagined Archimedes floating in outer space. Because Mr. Christides told us Archimides had said, "Give me somewhere else to stand, and I will move the earth."

I can see those geometry solids in front of me even now, and I still find pentagons, hexagons, octagons, you name it, intriguing still.

But had I ever seen an icositetrahedron (twenty-four sides, in Greek)? No, not before Athanasios David Xenakis showed me a two-dimensional surface mapped onto a three-dimensional solid.

David, who, with his son Benjamin, co-authored Photoshop 6 in Depth, is a polymath—he used to conjugate Latin verbs in our 7:00 a.m. college class by programing a main-frame computer, in Fortran!—and Photoshop guru.

David's collection of polyhedra include a multitude of shapes and sizes, featuring his photos of works of art taken on trips to Italy. So, when he asked if I had a photo of The Nativity that he could use for his icositetrahedron, I jumped at the chance.

Antonio Vivarini's 15th century, 69 x 43 inch, Die Anbetung der Könige, The Adoration of the Magi, Gemäldegalerie, Berlin. (Photo © Crè

So, David went to work with the icositetrahedron as the "solid," and as the "two-dimensional surface" The Adoration of the Magi, a large painting (69“ x 43“) in the Gemäldegalerie, Berlin, dating from 1419-20 by the Venetian painter Antonio Vivarini (1420-1484), in collaboration with his brother-in-law Giovanni d’Alemagna.

(I have shared a video of Vivarini's Adoration, and my visit in Berlin's Gemäldegalerie.)

Thus the Icositetrahedron Ornament was born. "It is mysterious and wonderful," David says, "and you certainly don't have to be able to pronounce it to enjoy making it. All that is required is patience, and precision."

David's icositetrahedron in progress with the tools of the trade.
What you'll need:

Icositetrahedron Premium Download
Photo-quality printer
Photo-quality paper (two sheets)
Cutting board
X-Acto knife
Metal straight-edge
Scoring tool
Glue stick
About 8” thin gift-wrap cord
Cutting surface

I like working on a commercially available cutting mat, but a stack of newspapers can substitute in a pinch.

I must also mention the importance of a well-lit working area: I like working in front of my west window, because it floods the attic with light in the afternoon.

But a halogen lamp—anything but fluorescent that tires the eyes!—or any other lamp that you can position to shed light on your work will do.

And mention must be made of being extra careful whenever you're working with sharp X-Acto knives. Keep the point protected in its clear shield when not in use. And, when cutting, use just enough force, and no more. You'd be amazed how light a touch is really required.

Assembly Instructions

1. Download and print the Icositetrahedron Ornament using the best setting your printer can achieve. There are two pages. Allow the prints to dry for several hours.

Before cutting out, from the front, carefully prick the paper at each corner node point (white circles). From the back, lightly score the paper between the relevant pin-points (dotted lines). Fold along each score line to make a crease. (Only half the ornament is shown here.)

2. From the front, carefully prick the paper at each corner node point (see the white circles on above diagram).

3. From the back, lightly score the paper between the relevant pin-points (see the dotted lines on above diagram).

4. Cut out the shapes as carefully and accurately as possible.

5. Fold along each score line to make a crease.

6. Repeat for second page.

7. Begin to glue the ornament by joining the two pieces at the sides indicated by the black dots outside the shapes (see diagram below).

In this assembly diagram, the right arrow indicates where loop is attached; center arrow the beggining; and the red circles mark the last tabs to be glued.

Additional information

1. The photographed model was printed on Epson Premium Photo Paper, item S041667, on an Epson Stylus Photo printer model R2400.

2. When scoring the paper from the back, don’t press too heavily. All you need is a line that will sufficiently compress the paper’s fibers to make the fold. Pressing too hard using the paper mentioned above will cause the ink to crack off along the fold line.

3. Begin the gluing at the place shown in the diagram above. This joins the two pieces together. Work your way around the object in both directions.

4. Although the glue operation is not difficult, it is time-consuming. It is best to glue one tab, allow it to dry at least five minutes, and then proceed to the next. There are 24 glue tabs.

5. As the shape becomes more complete, it becomes more and more difficult to hold the glue tabs together. I suggest working in both directions from the beginning until you reach the tabs, shown in the diagram above, marked with small orange circles. These three will be the last to be glued, and they will need to be done all at once (which will complete the shape). The last few glue tabs before these three can be accomplished by bending the section, shown as lightened on the right side of the diagram, in the wrong direction so that a small opening is left for the last few glue joins before the very last ones.

6. With the gold cord, tie an overhand knot at the ends to form a long loop. Tuck the knot end of this loop into the end of the gore shown in the diagram above, and then glue the tab.

7. If you see a few gaps after you have completed the gluing, use your X-acto knife to push small amounts of glue into the joins and then hold them until they are joined.

I hope you'll enjoy the [URL=""]Icositetrahedron Ornament[/URL], from

Thanks, David!

If only Mr. Christides could see this icositetrahedron now…

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