TallDave wrote:
http://en.wikipedia.org/wiki/Polywell
If the configuration is looked at as solenoids on the faces of a polyhedron, then the polyhedron chosen must have an even number of faces at each vertex, so that the polarity of the solenoids can alternate. Infinitely many polyhedra satisfy this property, for instance all antiprisms, 2n-agonal bipyramids, and all rectified (fully truncated) polyhedra. As can be seen in the picture, WB-6 is a cuboctahedron. Bussard's planned WB-8 would be an icosidodecahedron.
I'm not sure this is actually correct.
I don't know offhand about the planned WB-8 icosidodecahedron, but otherwise it's correct.
One key with seeing the WB-6/7/8/8.1 configuration as a "cuboctahedron" is recognizing that there are two fundamentally different types of "solenoids" present in the device. One type, the "physical" solenoid is obvious: they are the 6 stainless steel donuts that you see looking at the device. In each of them, there are large electric currents circulating clockwise around them when viewed from outside the device, so that all the North ends are pointed at the center.
The other type, the "virtual" solenoids aren't as obvious: Around each of the 8 vertices of the cube, there are three large currents from the three adjacent physical solenoids forming a triangle (a very curvy triangle, but a triangle) with the currents going counterclockwise when viewed from the outside. Since all the physics cares about is a circulating current around the axis of the solenoid, doing it in three unconnected segments is perfectly fine, and you get a solenoid without a coil.
The appearance of the WB-6/7/8/8.1 is cubic, with six coils on the faces of the cube, but the underlying physics is cuboctahedral, with inward pointing (physical) solenoids on the 6 square faces and outward pointing (virtual) solenoids on the 8 triangular faces. The vertices of the cuboctahedron are at the 12 points where the physical coils come close to touching. Around each of these twelve points are 4 solenoids, two pointing in, two pointing out, alternating. This arrangement, of alternating inward and outward solenoids is the key to Bussard's design for the polywell.
If you put an inward-pointing coil on all the faces of any polyhedron, preferably such that the coils touched just the midpoint of each edge, you'll get the critical aspects of the polywell. If the polyhedron is spherically symmetric, so will the polywell. With circular coils, you'll have portions of coils on adjacent faces nearly parallel with antiparallel currents, which causes a "line cusp" between them. With polygonal coils such that the coils come close at the corners of the coils rather than the sides, the size of the line cusps is reduced.