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I came across this shape last year, and referred to it in a book as the "Delta" fractal.

It's ... difficult to describe, so it's probably best if I post a link:

http://alt-fractals.blogspot.com/2011/02/baird-delta.html (http://alt-fractals.blogspot.com/2011/02/baird-delta.html)

The basic unit is a six-sided solid that looks a bit like two triangular shields glued together, back-to-back. When you iterate it, it generates Koch curves on all the faces, external and internal. I suspect that it might be the most fundamental 3D shape that has this property.

I was wondering: Does anyone know of any "prior art" for this thing?

The video appears to show 3 Tetrahedrons which are equally spaced around a common central axis

Hi Tomot! The three corner units aren't four-sided tetrahedra, but smaller rotated copies of the larger six-sided shape ... but now you mention it, yes, it's difficult to see this from the video.

Here's a wireframe view of the basic building block, and its first iteration.

The three smaller pieces on the right are perfect smaller copies of the larger shape on the left.

My laptop's working on a better, HD-quality video, but it might take a day or two to finish rendering.

The fractal only "works" when the solid has a very particular set of proportions, so the building-block would seem to be a fairly "fundamental" shape ... but I don't know what its name is, or if it even has a name.  

your right! its a Hexahedron.....2 Tetrahedrons stuck together.......googled that!  :)

Nice find. I haven't ever seen it before... this one generates a koch-like surface too, in a different way- http://www.fractalforums.com/ifs-iterated-function-systems/fun-with-koch-fractals/msg2630/#msg2630 (http://www.fractalforums.com/ifs-iterated-function-systems/fun-with-koch-fractals/msg2630/#msg2630)