A worldring has a similar surface area to a Gaian-type planet; it is sometimes called 'a world turned inside-out'
World Rings, as the name implies, are ring-type habitats which duplicate (as much as possible) all the conditions found on a Gaian type world - including total surface area under full centrifugal gravity. As such, World Rings occupy the middle ground between Bishop Rings and Banks Orbitals, and typically use technology from both.
Because a World Ring's radius is much larger than that of a Bishop Ring, carbon nanotube is not strong enough to overcome the hoop stress under full centrifugal gravity so some amount of magcarbon cabling is needed. To minimize the amount of costly magmatter World Rings are typically constructed like a radial tyre: Rings of magcarbon cables are run along the tops of the rimwall, like the beads of said tyre, while the more conventional carbon nanotube cables are laid across the ring, at 90 degrees to the direction of spin, from bead to bead. In most other aspects the World Ring will be constructed as a Bishop Ring or Banks Orbital would.
The greatest concentration of World Rings can be found in the Terran Federation system of Magal (home system of House Magal). These orbit the system's star in a single dyson ring swarm that is collectively called "The Ring of Ages." The goal of the Ring of Ages is to recreate the surface features and life of Earth; not just as the terrans remembered it but as it was throughout its history. To this end the Magals have devoted one World Ring to each of the eras, periods and epochs of Earth's geologic time scale. Also within the Ring of Ages are clusters of rings for the "Ages of Man" which cover the prehistorical periods, the historical periods and the mythological periods (such as the antediluvian period, the Atlantian age and the heroic age). There is even a cluster of Dixolutionist rings that explore alternate and future evolutionary histories. Magal World Rings are constructed more like a belted radial, with additional strands of magmatter in the ring floor, because it was also important to them to get the map proportions right. Their World Rings all have a radius of just 6,400 km (6,378.16 km inside at sea level) but are 12,728 km wide and use cylindrical equal-area projection to lay out the surface features.
Because Magal World Rings are not true rings but actually short cylinders they need additional stabilization to prevent tumbling. Some of this comes from fine tuning the distribution of mass, concentrating it towards the "equatorial regions" of the World Rings while lightweighting the rings near their rim-walls. This has been achieved by foaming the materials of the lithotorus, and shallowing the hydrotorus, near the rim-walls. Even the rim-walls themselves are, for the most part, just sheets of carbon nanotube cables hung under tension from the beads like curtains. Also, active stabilization has been gained by enlarging the rings' hubs into smaller counter-rotating cylinders: Magnetically linked to their larger cylinders these inner cylinders hold all of the out-of-period populations, the hab minds, power generation, etc. The underside of an inner cylinder also provides the lighting effects for their outer cylinder. Covered with an optical phased array the inner cylinder can project not just sunlight but also moving images of Luna, the planets, the stars and anything else that might be needed. And by accelerating/decelerating one cylinder against the other "tides" can be generated in synch with the movements of the "sun" and "moon."
There is a second type of World Ring, one that doesn't need magmatter and can therefore be built by modosophont-ruled polities. This type of World Ring is actually more like a small topopolis; a torus that rotates around the long axis of its small circle rather than the short axis of its large circle. The smaller(tube) diameter of the torus can be any size the polity has the tech for but to be classed as a World Ring the larger(ring) diameter has to be great enough to provide a total surface area equal to that of a Gaian type world under full centrifugal gravity. For example, the combined surface area of 163 Bishop Rings (1,000 km radius & 500 km width) is equivalent to that of Old Earth. If these were stacked, and looped, the torus would be almost 30,000 km across but the biosphere would not be continuous. On the other hand, if a small topopolis were placed around Old Earth in a geostationary orbit it would only need to have a "tube" radius of 306 km to equal the surface area of the world below it. As can be seen, with this type of habitat a larger ring diameter results in a smaller tube diameter which allows for greater engineering freedom; there is a wider choice in the materials (such as Pandifico) and/or technologies that can be used to overcome such problems as deformation or kinking. Indeed, at the smallest tube diameters it is even possible to replace short segments of the tube with materials that don't just stretch, as the ring's inside circumference becomes its outside circumference, but actively expands and/or contracts to drive the tube's rotation.