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Worldbuilding - Dimensional Cosmology

Fantasy games like DnD include the presence of alternate dimensions or "planes". The presence of these planes may be very important to your world, and should you decide to use them you should plan for how they work, how they affect the primary plane of existence, and how they can be reached.

Are there other dimensions, planes, or worlds?

The existence of other dimensions has heavy implications for your setting. The settings of Warhammer and Warhammer 40k both have an alternate dimension called "The Warp", which is the home of otherworldly horrors like demons. Dungeons and Dragons worlds largely share a singular cosmology, often called "The Great Wheel". Norse mythology depicts several worlds as parts of the "World Tree". The presence of these dimensions has far-reaching implications for the way the world works.

What are they?

Alternate dimensions can be many things. Some or all of the following examples might exist in your setting:

Where are they, and how does someone reach them?

"Where" is a difficult question to answer in many interpretations of extra dimensions, but in others it's a perfectly valid question. Other dimensions might be places which you can walk to, but which are very different from the normal world. Some planes mirror reality; in the Warhammer 40k setting, The Warp is an omnipresent alternate dimension which you can reach from anywhere, and which occasionally bleeds into the real world (especially around the Eye of Terror). In DnD the Etheral plane coexists with the material plane, and ethereal creatures can see into the material plane like looking through a fogged window. Other planes in DnD are far-off places which must be reached by powerful magic or by traversing a series of portals.

The means by which you reach other dimensions helps to inform how they interact with the primary dimension. In Greek mythology, you could reach Hell by descending certain caves in some mountain ranges, and you could reach Olympus by climbing mount Olympus. In the Halo universe, "slipspace" is reached by tearing a hole in spacetime with complicated device called a "Shaw-Fujikawa Translight Engine". In DnD, different dimensions can be reached with powerful magic, or by traversing portals or places where the barriers between adjoining dimensions are weakened and unsuspecting inhabitants can fall between the material plane, the shadow plane, and the feywild. In the Spelljammer setting, planes are contained in "crystal spheres" which can be traversed by powerful ships called Spelljammers. Assuming that these means of transportation are two-way, if your alternate dimensions are inhabited you may need to consider what happens when the inhabitants of those dimensions enter the primary dimension.

Examples of Planar Cosmology

Examples

Example 1 - Shadow of Olympus

The Olympus model is perfect for a greek-themed setting. Hades can be accessed through certain cave networks which lead to the river Styx, and Olympus is a ridiculously huge mountain at the center of the world with the seat of the gods at its summit.

I want to include elemental forces (possibly as the origins of the titans, who the greek gods don't particularly like), so let's include the elemental chaos as a flat ring around the edge of our world. Maybe the elemental chaos is a churning mass of chaos barely held back from the fraying edges of the material world. because I want to use this setting with something like DnD or Pathfinder, let's say that there's also an ethereal plane for ghosts to hang out in, and the Abyss hangs off the bottom of Hades, and contains awful things like demons and titans, locked away far from the world above.

Example 2 - Space Grease

Dieselpunk in space doesn't really need other dimensions. We might consider a "hyperspace" or "war space" concept for FTL travel, but I think it's fine for there to be some sort of real-space FTL travel mechanism, making other dimensions unnecessary.

Example 3 - Heroes of Tonesvale

Alternate realities are a classic plot element in comic books, but it's rare to have a consistent, defined set of alternate dimensions. There might be some dimensions which exist largely for the theme of specific characters (like the weird dimension where Doctor Strange apparently likes to hang out), but they can be created and discarded when specific characters need them, much as they are in the world of comic books.