Unfolding Humanity Exterior

Unfolding Humanity

For centuries, the work of the mathematician and the visual artist are viewed not only as incompatible, but held in tension. Mathematics is attributed to Platonic notions focusing on abstract ideas and theoretical structures. The visual artist, on the other hand, is relegated to works of the hands, dealing with the concrete and the tangible. In trying to bring these worlds together, we should be wary of easy shortcuts to a complex issue, valuing both true artistic vision and rigorous mathematical sophistication. And so we ask: how can vibrant, contemporary art be produced that deals with vibrant, contemporary mathematics?

Unfolding Humanity, a massive, interactive sculpture, is one attempt in answering this question.


Unfolding Humanity also calls attention to the connection and contrast between humanity and technology. The structure shows the humanity still existent within technology. The faces which are folded against the structure represent the encapsulation of humans by technology; we are cut off from one another by technology and are increasingly only communicating with one another through this encapsulation. Our sculpture serves to remind us that even as the web of technology grows, that inner foundation of humanity will always be present.

Its design is inspired by the work of USD students Jordan Abushahla, Nick Bail, and Eugene Wackerbarth.

Unsolved Mathematics

Unfolding Humanity alludes to Albrecht Dürer's 500-year-old unsolved problem: can every convex polyhedron be cut along some of its edges so that it unfolds flat into one piece without overlap? Every attempt to do so has resulted in a positive answer, but mathematicians are still divided over whether this is always possible. Our exhibit offers an example of such a positive answer, by allowing participants to unfold a dodecahedron in a way that satisfies the unsolved problem.

The Shape of Our Universe

In ancient times, our planet was thought to be flat. Today, we know the shape of the Earth, having traversed it and observed it from space. But what about our universe? Is the universe, though unfathomably vast, finite in size? And what is its geometry — perfectly flat or bent and curved? Revolutionary data from special satellites revealed wonders (Luminet et al., Nature, 2003):

"The standard model of cosmology predicts that the universe is infinite and flat. However, cosmologists in France and the US are now suggesting that space could be finite and shaped like a dodecahedron instead. They claim that a universe with the same shape as the twelve-sided polygon can explain measurements of the cosmic microwave background – the radiation left over from the big bang – that spaces with more mundane shapes cannot”

Although the data we have been able to measure thus far fits well with a flat universe, it is also consistent with positively curved, hence finite, shapes such as the Poincaré dodecahedral space. Our interactive sculpture gives participants an opportunity to enter a small finite universe modeled on the Poincare dodecahedral space, in order to witness the complex beauty of a universe where light folds back upon itself. It is an opportunity to experience the marvel of a small space with finitely many objects becoming wonderfully vast, with infinitely many images of humanity and star-like lights scattering through the night.



At roughly 10' cubed, this dodecahedron will be built of pentagonal acrylic faces on top of a metal interior framework. Hinges connect some of the faces to give the structure the ability to interactively unfold flat, using a series of engineered torsion springs, cables and winches.

Exterior faces are dark green acrylic etched with characters illuminated by trailing LEDs invoking the iconic Matrix animation, whereas interior faces of reflective acrylic mirrors create a kaleidoscopic image of people. The frame and the pentagons themselves are illuminated by light from LED strips on the outside and inside. When unfolded (40’ x40' x10'), the metal dodecahedron framework is still standing while the panels are arranged as petals of a flower along the ground below it.

Radically Engineered

Our structure is carefully engineered and tested by a recently graduated USD mechanical engineering, physics, and mathematics major, with CAD and machining support by two additional USD engineering students. These three, under the supervision of an USD Engineering professor, will assure that the structure is designed to handle the stresses of any real world interaction or environment.

Cables feed from each of the 5 furthest pentagons, through pulleys on the metal framework, to instantly locking brake winches which are specifically designed for lifting. This holds the structure in place in any configuration between fully open and fully closed. The winches are chosen at a gear ratio that allows the faces to be folded at a safe speed. All cables on the structure will be illuminated by spotlights shining along their length, and all winches will be similarly illuminated.

Damping and angle-limiting hinges are used to add further control to the folding motion. The hinge system is designed so that the bottom pentagons unfold first before opening the attached top pentagons, mimicking the unfolding of flowers in nature. This minimizes pressure on the bottom most hinges and reduces the weight hazard.


Returning Lighting Artists

The people responsible for programming the mesmerizing animations of last year’s highly regarded multimedia installation The Journey Project are teaming together again to make the illumination of this sculpture a captivating experience which helps express the philosophy of the piece.

The metal dodecahedral skeleton will be continually lit on both inside and outside by programmed LED strands which respond interactively to the level of openness of the panels.

LED lights will form an interior layer for each pentagonal face. The exterior faces will be dark when the dodecahedron is folded open, coming to life as each face is closed to the metal skeleton. When a face closes onto the frame, the falling character animation from the Matrix will come alive, indicating that a further step in the enclosure of a human participant has taken place.

The acrylic mirror faces on the interior of the structure will remain unlit, to allow the light from the frame to create intricate patterns in the many reflections.

Who's Buying It

We've raised >$27k of our $35k budget. Thank you to SDCAP & USD’s support via its Fletcher Jones Endowment!

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Visit and donate on our crowdfunding page, with rewards including:

  • T-shirts, postcards, and photographs
  • Awesome swag to be developed by J. Good

We plan to organize two large fundraiser events for this program. A partial reason is to raise support, but another (more important) reason is to inform the public (from the academic to the artistic side) of our vision. These fundraisers will bring together two communities, whose goals intersect at our project: bring deep thought in beauty, at the intersection of art and mathematics.