George W. Hart

Wormhole is a 27-inch diameter, stainless steel sculpture that I designed to be assembled as a sculpture barn raising at the 2010 Gathering for Gardner conference in Atlanta. The page explains the design and shows the test fit and preparations before the group assembly at the conference. The exterior of the design contains twelve symmetrically arranged four-armed “galactic” forms, arranged with octahedral rotational symmetry in the planes of a rhombic dodecahedron. These twelve parts are identical, except that six extend downwards  to a base. The worm-like arms come in two shapes, carefully calculated to pass around their near neighbors, and then connect to a further neighbor (of the other shape) in an orthogonal plane, to give a swirling “worm ball” effect. The orthogonality of the outer connection planes allows for a simple tab-and-slot assembly mechanism. Inside the outer form is a second level at half scale and inside that is a third layer at quarter scale.  This could be continued, but three layers are enough to create a visually interesting interior space and suggest an infinite geometric series leading towards a singularity at the center.

There are six 4-fold spiral openings, which allow you to find the inner layers and see the "wormhole" effect.

Here are the thirty six laser-cut parts laid out before the assembly, twelve in each of three sizes.

The inner core consists of these twelve small-size components.

The core is best understood as three copies of this square arrangement. 
If you think of this as a cube, then the core structure is like the interlocked
compound of three cubes seen on the left tower in Escher's Waterfall.

The twelve-part core looks very different when viewed along a 4-fold axis.

The exact same 12-part structure looks different again when viewed along a 3-fold axis.

In the above image, you can see the inner and the middle layers, twenty four parts total.
The tips of the inner layer parts penetrate through the centers of the second layer parts.

Above are the first and second layers viewed along a 4-fold axis.

And above are the first and second layers viewed along a 3-fold axis.
The tabs are not bent yet, as this is just a test fitting. At the actual assembly,
I'll twist each tab slightly, locking parts together so they hold permanently together.

Adding the twelve outer parts, the sculpture is complete in three layers.
Note how the tips of the middle layer parts penetrate through the centers of the
outer parts. This view along a 3-fold axis shows how the three layers are concentric.

I bent six brackets (and a spare) to connect the base to a pedestal.
A small spot weld locks the 120-degree angle. (Thank you, Lester Orlick.)
This is the only place where bolts or welds are used; all other connections are tabs.

Before cutting any metal, I made a long series of computer models and renderings to work out the many details of the design.

I also made a scale paper model using the same tab-based connector system. 
Here it is under construction, with the two inner layers complete and parts of the outer layer being added.

The complete paper model is eight inches tall.

I made hundreds of 1.4-inch models of Wormhole that illustrate some of its geometric properties. 

The models are made of nylon, by selective laser sintering, then dyed in one of several colors.

Here is one close-up.  I find them pretty cool.

And here's one all packaged in a clear plastic box, along with a small sheet of information.

And to end, here is one final view of the real thing, Wormhole.
I then disassembled it and shipped the parts to Altanta for the G4G9 assembly event.

Copyright 2010, George W. Hart