We spent the weekend at Bald Head Island with family… what a great way to say goodbye to summer. In the BHI Conservancy shop we found a tempting book/kit: M. C. Escher Kaleidocycles: An Illustrated Book and 17 Fun-to-Assemble Three-Dimensional Models.


According to the publisher:

A Kaliedocycle is a three-dimensional ring made from a chain of solid figures enclosed or bonded [sic] by four triangles. These kaleidocycles are adaptations of Escher’s two-dimensional images of fish, angels, flowers, people, etc., transformed into uniform, interlocking, three-dimensional objects whose patters [sic] wrap endlessly. Kaleidocycles contains a 48-page book with over 80 reproductions and diagrams, assembly instructions, and a fascinating discussion of the geometric principles and artistic challenges underlying Escher’s designs and their transformation to three-dimensional models; and seventeen die-cut, scored, three-dimensional models (11 kaleidocycles and 6 geometric solids).

I was so tempted to buy the set, but I resisted. You might enjoy finding some similar projects online for free (let me know if you find any). Anyway, on to the assignment at hand.

Current Assignment: Monday, September 21
Read: Sonata for Unaccompanied Achilles and Chapter III: Figure and Ground
Listen: Sonata No. 1 for solo violin: Adagio (BWV 1001). If an accompanied version of this exists somewhere, I don’t know where to find it.

Summary of Sonata for Unaccompanied Achilles:
This Dialogue imitates the Bach Sonatas for Unaccompanied Violin. In particular, Achilles is the only speaker, since it is a transcript of one end of a telephone call, at the far end of which is the Tortoise. Their conversation concerns the concepts of “figure” and “ground” in various contexts –e.g. Escher’s art. The Dialogue itself forms an example of the distinction, since Achilles’ lines form a “figure”, and the Tortoise’s lines – implicit in Achilles’ lines – form a “ground.”

Summary of Chapter III: Figure and Ground

The distinction between figure and ground in art is compared to the distinction between theorems and non-theorems in formal systems. The question “Does a figure necessarily contain the same information as its ground” leads to the distinction between recursively enumerable sets and recursive sets.

Discussion Question (just one):
Explain Figure 18 (p. 71) as you understand it to your roommate, co-worker, significant other, or even a random passerby.

Figure 18

Up Next: For Thursday, September 21
Read: Contracrostipunctus and Chapter IV: Consistency, Completeness, and Geometry
Listen: Contrapunctus 19 from the Art of Fugue (BWV 1050). This performance abruptly ends in the same place that the score ended due to Bach’s death. Bach left his name in the music, as the German notes B-A-C-H, a few measures before the end.

5 thoughts on “

  1. Ros

    I thought they looked familiar! I googled kaleidocycle and found that they are also called flexahedrons. I had a book of instructions for making these when I was a child. Lots of fun, though mine never really worked properly (no precision in my measuring, cutting or gluing).

  2. Karyn Post author

    Hi Ros,

    Thanks for sharing about the flexahedrons of your youth! I’m still looking for some free patterns to download before I give in and buy the book.


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