From void into vision, from vision to mind, from mind into speech, from speech to the tribe, from the tribe into din.

Monday, August 27, 2007

M. Preston Burns, Pandora's Box, Experiential Geometry

I've been experimenting for over thirty years with geometric models. Recently, my collaborator and the man who introduced me to this work, M Preston Burns, died and I have been going over his portfolio and papers. Mel or, as I knew him, Bud Burns worked primarily with the cube and the tetrahedron. He divided the square faces of the cube on the diagonal revealing the equilateral tetrahedron packed inside. He cut and hinged the cube and made a winged tetrahedron, eight hinged equilateral triangles, to fit inside. Then he filled the corners with ToyBlox, wooden forms which demonstrated the two-fold symmetries of the cube and tetrahedron. He called it Pandora's Box and demonstrated six inch, one foot, four, six, and eight foot models publicly since around 1970 when he built the first prototype.

This is a short video of what was probably his last presentation of Pandora's Box :

The advantage of working with these models is that they teach geometry and symmetry experientially, without the need of numbers or words. These forms are inherent in dimensionality. They are true, in the way a carpenter measures true - straight, level, plumb. By having three dimensional models you can turn around in your hands, you develop a hand-eye relationship with fundamental geometric forms. The cube and tetrahedron models of Pandora's Box teach the relationship between the right triangle and the equilateral triangle as well as two-fold and three-fold symmetry viscerally. This is full contact mathematics.

If you are interested in this kind of experiential geometry, there will be a symposium on "Synergetics and Morphology" at the Rhode Island School of Design on November 3 and 4, 2007 in Providence, RI. Further information is available from the Synergetics Collaborative

Another short video of Bud outlining his symbology system:

His friends will remember M Preston Burns at the current exhibit of his work in Cambridge, MA at Toscanini's Ice Cream, 899 Main Street on Tuesday, August 28 at 7 pm.

You can see more of his drawings at Bud's Gallery

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Monday, August 06, 2007

Dancing the Cube in Jamaica

This is a video Julie of Videosphere took December 2006 of Azisu, Nikita, Chaka, Werner, and Bud playing with a magnetic Quanta Cube, a cube made of 72 A and B Quanta. The A and B Quanta are the smallest common symmetrical tetrahedra of the regular tetrahedron and octahedron, two of the Platonic Solids. They were first discovered and analyzed by R Buckminster Fuller and Dr Arthur Loeb. Both the A and B Quanta come in left-hand and right-hand pairs, they are mirror images of each other, enantiomorphs. As positive/negative pairs, they are perfect for magnetic coupling and there are magnets at the centers of each of the four faces of each Quanta in the Quanta Cube, 288 magnets in all.

The Quanta Cube is derived from the work of M. Preston Burns, Bud, the skinny old dude in the video, who built his first Pandora's Box nearly 40 years ago. We worked together building various models of the box at different scales from eight feet to six inches and demonstrated them before the public and as part of an arts curriculum with Tribal Rhythms. Bud dissected a cube along its diagonals, hinged the pieces, and packed a "winged tetrahedron," a hinged tetrahedron with eight equilateral triangles, in the center. He filled the corners of the cube with ToxBlox, illustrating the symmetrical divisions of the cube. That is Pandora's Box.

One day, I was playing with a set of A and B Quanta I had made and discovered how to fill the box with A and B Quanta. Later I developed the magnetic coupling system with Carl Fasano of RISD.

More on Synergetic geometry and R. Buckminster Fuller at

More video of the Quanta Cube at

More geometry video from RISD:

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