Total invulnerability -a major goal for any being of power. I made an earlier character aiming for this objective, but its method for evading divinations (using the position of an object in a looping teleportation circle chain as the basis for who gets control, so the identity of the controller isn't absolute) proved controversial. So here I am with a new and improved version - I present: The Sphere!
So first, the starting conditions. Let's say we have an epic-level Thrallherd Nomad Psion, with wizard and artificer cohorts, who's been powerleveling via Scry & Die, so has effectively limitless XP and resources.
Now, the building: It is a spherical structure with no entrances, and a hollow interior. This interior contains certain mindless undead (detailed later) and certain magic items (also detailed later). Any empty space is filled with Gelatinous Cubes, so it becomes impossible to teleport inside.
The magic items include 48 Lyres of Building, which are played by some of the undead to make the building indestructible 24-7. The building itself is also enchanted by the artificer, so it cannot be affected by powers which only work on nonmagical objects. Lastly, the Wizard then throws up a double-layered permanent Epic Ward, which directly blocks the Afflict, Destroy, Dispel, and Transport seeds (treating them as 10th level spells). Since the Ward is double-layered, each Ward protects the other from the Destroy and Dispel seeds. The dispel DC for these wards is boosted so high that no non-epic spells can dispel it.
Now for the anti-divination part. The Psion builds up a Weird Engine (Air Weirds under his control that can repeated cast Contact Other Plane) and uses the result power to figure out how to replicate his consciousness as a very large number of separate, simple, components that can respond to sensory imputs by providing an instruction and/or activating other components.
Once this task is complete, he sets about creating these components, along with an automatically resetting Dimensional Oubliette (
http://dsp-d20-srd.wikidot.com/dimensional-oubliette) trap. Once the components are complete, he devises a way to feed them sensory input and to deliver their instructions to the mindless undead operators, and to the Dimensional Oubliette trap. Lastly, he sends all components not actively engaged in thought into their own Dimensional Oubliette, where their existence "is merely theoretical" they "do not exist conventionally" and divination/clairsentience effects used on them "fail as if they were used on something nonexistent". When a component activates another, it uses the Dimensional Oubliette trap to free them, and each component uses the trap on itself to go inactive.
This done, the trap is used to send the psion, all his cohorts and followers, along with the Air Weirds and anything else used in construction, to a Dimensional Oubliette. Now, the component-based "brain" is all that remains, and since the vast majority of it is in the Phantom Zone at any given time, its operation is literally inscrutable.
Now, for the fun. We have an indestructible sphere with an inscrutable operator, so what do we do with it? One idea: let one of the mindless undead have over 20 HD, use Psychic Reformation to give it Throw Anything and Distant Shot(
http://www.d20srd.org/srd/epic/feats.htm#distantShot) (use epic spells to enhance its physical capabilities as needed). Give it flight, and a way to see through the stone, and it can throw the Sphere at anything it can see, for massive damage.
If you have any more ideas for undead operators or magic items to put in the sphere, feel free to submit them. Thanks for reading!