Eidopolis
An eidopolis (pronounced /aɪˈdɔːpɵlɪs/, plural eidopoles, /aɪˈdɔːpɵliz/) is one of the cities that makes up Eidecia. Each eidopolis seems to be a representation of a single concept, or perhaps a single interpretation of a concept, be that concept an abstraction such as time or knowledge or a concrete object, or category of objects, such as puppets or mist. Although each eidopolis does seem to be located in a particular world, the eidopoles also connect to each other in a complex network. Every known eidopolis is much larger than the vast majority of other cities, and while there is certainly trade among eidopoles and (to a much lesser extent) between eidopoles and the worlds they impinge on, each eidopolis remains sufficiently self-contained to be possibly considered a world of its own (albeit a somewhat small one).
Residents of Eidecia do not generally use the word "eidopolis". More commonly, Eidecians will just refer to "the Cities"—cities outside Eidecia rarely meriting mention anyway. If for some reason they do need to explicitly refer to the eidopoles as opposed to other cities, they are more likely to call them the "True Cities", the "Inner Cities" (as opposed to the "Outer Cities"), or the "Object Cities". (This last is in contrast to the "Image Cities" outside Eidecia, the idea being that the eidopoles are the true reality of which all else is only a reflection—an idea, needless to say, that non-Eidecians are unlikely to agree with.) The only people who are at all likely to regularly utilize the term "eidopolis" are æalogists and certain other scholars.
Geography
To a casual visitor, it may not be obvious that the layout of an eidopolis is neither fixed nor Euclidean. This is, however, the case; if careful measurements are made of the lengths and angles of the streets and building walls, many anomalies can be found demonstrating that the space of the eidopoles must be curved. A triangular park or building with straight sides may have angles that add up to more or less than 180 degrees; streets parallel at one point may, without curves or bends, intersect at another. The curvature of the city's space is subtle and irregular, but it is there. Nor is the city even necessarily simply connected; in some cases attempting to map out the city produces an arrangement of elements that can only be made sense of by assuming the topology of city's surface is not planar, but has handles and perhaps, in rare cases, scambons. Certainly every eidopolis has a much larger area than would be possible from its perimeter were it merely a flat surface.
This would make it difficult enough to produce an accurate map of an eidopolis; what makes it impossible is that the geography of an eidopolis isn't even constant over time. The topology of most of the cities rarely if ever changes—that is, a given street will always connect to the same other streets, in the same order; a particular building will always have the same neighbors—but distances and directions often do. The changes are slow and subtle, generally unnoticeable except over long periods of time, but over several weeks, say, a particular street may grow or shrink in length by twenty meters, or in width by one, or two streets that used to meet at a right angle will gradually come to meet at a slightly different angle instead. Sometimes these changes seem to be in response to events or trends in the city's population; if many people move into a particular neighborhood, that neighborhood may grow slightly to accomodate them. Other times, it appears to be random.
While no static map can therefore be made of an eidopolis that is completely accurate, however—at least, not for more than an instant, as the eidopolis constantly changes—because the changes are slow and the topology is conserved maps may be made that are accurate enough for all practical purposes. Even the projection of the cities' weird topologies onto a planar map still can produce a useful result; if some of the angles and distances don't quite match up, at least the relative positions of landmarks are close enough to enable one to use a map to find his way around. Dynamic maps have been produces that detect the movements and alterations of the eidopoles, and change themselves accordingly, but such maps are rare and expensive—and for most purposes they're considered more status symbols than necessities.
Beyond the eidopoles
Each eidopolis is, at least in a sense, situated in a specific world, and it is possible to travel between the eidopolis and the surrounding world relatively easily. Most of the eidopoles are walled, separated from the surrounding world by stone, metal, or other barriers, but even so gates generally exist in the walls to allow passage between the city and its exterior. Furthermore, there is, in most cases, nothing particularly supernatural about the walls themselves, and it may be possible to break through or pass over or under them. Still, the difficulty of doing so is sufficient that the vast majority of traffic in and out of the eidopoles passes through the city gates. A few eidopoles have no walls and are open to the outside world, but this is rare, perhaps because of the insularity of many Eidecians, but also perhaps because it makes the difference in geometry inside and outside the eidopolis more patent and disturbing.
Despite the ease of travel between the eidopoles and the worlds in which they are set, most eidopoles have little commerce with other inhabitants of those worlds. They are typically located in out-of-the-way, near-inaccessible places and unknown to the majority of the worlds' populace. They may be on islands far from land, deep underground, hidden in a trackless wasteland, or otherwise situated where other men are unlikely to travel. Some few may stumble upon them, but even to most of those they remain strange mysteries, perhaps giving rise to tales and legends but never becoming the subject of regular visits. In those rare cases that eidopoles are near other communities, they still have little contact with them, being fearfully regarded as cursed places closed to man and best avoided. There are exceptions here, some few eidopoles that are well known in their surrounding worlds... such as Walgaraw, which engages in extensive trade with its neighboring communities, and Gathen, which rules the world where it is located.
The eidopoles also have other exits, however, which lead to pocket planes called pathnodes. Each pathnode generally connects to several eidopoles, furnishing a means of traveling from one eidopolis to another. The entrances to the pathnodes are located within the cities, resembling (usually) walled-off courtyards from the outside, though on the inside the pathnodes can be much larger than the circumference of the walls would indicate. In fact, once past the threshold into the pathnode, things seem reversed and the city seems to be a small, walled-off structure within the pathnode. In most eidopoles, there's much more traffic through the pathnodes than there is through the city gates; many more people are interested in traveling to other eidopoles than in visiting the rest of the world in which their own eidopolis is located.
In any case, although travel between eidopoles is far more common than travel between an eidopolis and its surrounding world, there are many residents of the eidopoles who never leave their home city at all. Each eidopolis is so enormous and multifarious that it has enough variety in its contents to satisfy even the most eclectic and adventurous soul, and it's quite possible to live a fruitful and stimulating life entirely within the confines of a single eidopolis. The eidopoles may be individually much smaller than a typical mound, but they're still rich enough to essentially form entire worlds in and of themselves. Nevertheless, there are some individuals who do travel between them, either to engage in trade, to study their differences, or simply to see what lies beyond their own homes. Even they, however, rarely find reason to leave Eidecia.
Governance
Each eidopolis has a single leader, who goes by a different title in each case. (There are possible exceptions, such as Gathen with its Ultimate Court, but even there it may very well be that there is a single leader who presides over the Ultimate Court but remains unknown to the general populace.) The origin of the city leaders is unknown, as is their true nature—the leader of each city seems to be a unique, inhuman entity with strange magical properties. No standard word has become current to refer to the city leaders in general; each one has a different individual title, but there is no collective title to refer to them as a whole.
Each leader has special powers that allow him to better exercise his rulership. The extent of these powers is unclear, but for all practical purposes within their cities the leaders appear to be more or less omnipotent—if some of them have particular abilities they like to use most often, this doesn't mean they don't have many other abilities as well. It has been proposed that the geography of the cities itself may be under conscious control of their leaders, responding to their will rather than simply changing randomly; this has never been proven, but is certainly consistent with what little is known about the leaders' link with their cities.
No city is known to have changed leadership within living memory (except possibly special cases like Aarven), and it's not even clear whether this is possible, or whether the city leaders are somehow so tied into the cities that they rule. Nevertheless, there are certainly those who try to destroy the city leaders and usurp their power for themselves. There is no known case of this happening, though it has been whispered that perhaps some have succeeded in overthrowing their city's leader... and have taken that leader's place themselves, the very memory of all Eidecia's populace altered to remember their new leader as having always been there. It's also not clear whether it's possible for the leaders to leave their cities; certainly there are no reliable reports of any city leaders having been encountered outside their dominions. Even if they don't have the power to travel outside their cities, however, within their cities the leaders' power seems virtually limitless. Even gods while within the eidopoles are subject to the power of the city leaders.
While these mysterious leaders are the ultimate power and authority in the cities, they aren't generally concerned with the day to day business of administration. Most cities have their own local governments that take care of passing and enforcing laws and other mundane tasks of governance. They certainly bow to the desires of the real leaders when these choose to make their wishes known, but for most purposes the secondary government is left a free hand in running the city's business, with the leaders only stepping in occasionally to make some particular demand.
Trade
Despite its size and complexity, an eidopolis doesn't necessarily find it easy to provide on its own for all the wants and needs of its inhabitants. The eidopoles do engage in trade to supply some necessities and luxuries—mostly with other eidopoles, but also with inhabitants of pathnodes, and in some cases even with those living on the worlds outside Eidecia.
One of the most important objects of trade is food. Most urban settings are not conducive to the production of foodstuffs, though some manage to produce food in various unusual ways—by creating it magically, by growing edible fungi in underground areas, or by the maintenance of floating gardens above the cities, for instance. Still, while there are some cities that manage to produce enough to fill their needs, most must import it from elsewhere. Those few cities that do produce their own food may produce enough excess to trade some with their neighbors; Fareë, City of Abundance, for instance, is a major exporter of food of many kinds. Much food is also imported from the pathnodes, some of which have soils and climates conducive to farming. The world outside the eidopoles may also supply some food, in those rare cases when trade is conducted between an eidopolis and its outer world.
Merchants, or their hired agents, are among the few who do find reason, then, to travel between different eidopoles, and make up much of the traffic through the pathnodes. This is not an easy profession; to be successful, these merchants must be familiar with the times and customs of several different eidopoles, and be able to keep track of the financial trends in each. Most merchants therefore specialize in trade between a handful of cities, perhaps only two that they know particularly well, perhaps as many as four or five if they're very good at what they do. A very few merchants, or mercantile networks, manage to be well acquainted with a large number of different cities, and carry out large scale trade between them, on whatever routes and in whatever goods seem most profitable at the moment. This level of trade is quite difficult to carry out, but can be enormously lucrative to those who are capable of it. Some of Eidecia's largest and best known mercantile networks include the Tesseract, the Tidings, the Invisible Company, and Hallot & Dusk.
Formation and dissolution
While most Eidecians think of the Cities as eternal and immortal, it seems that new eidopoles do appear from time to time. Nime, the City of Creation, infrequently buds off new cities, but this doesn't seem to be the only way that new eidopoles form. The details are unclear, but the best current scholarly consensus is that on very rare occasion Eidecia "adopts" an existing city into it. According to one tentative model, a pathnode first opens onto some point in the city, and then the city is gradually assimilated, its physics and geography changing to conform to that typical of Eidecia. Some scholars propose a slightly different model in which, rather than part of another world being assimilated, the pathnode connects to another world but there creates an embryonic eidopolis that gradually expands, producing as it does so distortions in the world around it that eventually smooth out. No accepted theory has yet been proposed as to the origin of the city's leader.
Although no eidopoles are known to have been permanently destroyed, or to have suffered any sort of disappearance or dissolution analogous with the death of a living thing, there are stories of eidopoles being "lost". Some eidopoles, it is said, have become severed from the rest of Eidecia, disconnecting from their pathnodes and remaining accessible only through their surrounding world, or through magical portals. Accounts vary regarding the reasons for this phenomenon, but it is most commonly ascribed to the will of the eidopolis's leader, and is sometimes said to be possible only for eidopoles whose "theme" relates in some way to separation—or perhaps, conversely, to connection. In any case, if any such lost eidopoles do exist, it seems questionable whether they could ever be found... although the possibility has been suggested that perhaps their connections to the pathnodes may not have been completely severed, and that maybe there does remain some hidden way to reach them.