This plaiting method is usually attributed to Marvin Hardy. The most basic product of circular plaiting is what Marvin refers to as a sunburst in his book The 260Q Decorator. The sunburst drawings below are taken from Twisting History - Lessons in Balloon Sculpting by Larry Moss, where it is used in a bird cage sculpture.)
Several balloons are twisted together at their midpoints. The actual number of balloons used can vary. In this example, three balloons are used. The balloons are then placed on a flat surface and arranged so that the angles between adjacent balloons are equal. These balloons can be thought of as the spokes of a wheel, radiating outward from the hub.
While not necessary, a small ear twist made in one of the balloons at the hub will help to hold all of the spokes flat. Additional balloons can then added in a circular pattern around the hub. Start by tying the nozzle of an inflated balloon to one of the spokes, approximately one inch from the hub. The first few times you do this, use one color for the spokes and at least one other color for the rings. It is much easier to follow the pattern you are making when different colors are used.
Make a one inch bubble and twist it into the next spoke. Continue around, connecting successive bubbles until you return to the first spoke. Break off any remaining ring balloon and tie it.
To form a complete sunburst, continue adding new ring balloons as you did the first. Just tie each one to a spoke, then twist ring bubbles and connect them to successive spokes. As you progress outward, each new ring is started with a new balloon. As the sunburst diameter grows, you will eventually reach a point where the circumference of the sunburst is greater than the length of a single balloon. This isn't a problem since any place that a twist occurs, a new balloon can be tied on.
Sometimes, for different effects, you'll want to add rings spaced further apart than pictured above. Larger creations can be made with fewer balloons if this is done.
We can't have 6.28 spokes, so we round that down to 6 spokes and slightly increase the length of the bubbles in each ring to compensate.
See a video clip demonstrating the information on this page.