Awesome

FulldomeCameraForUnity5

Fulldome Camera plugin for Unity 5.6

To run a Fulldome game, this plugin needs two prefabs in your scene. A Camera Rig and a Controller.

Place FulldomeCamera/Prefabs/BlendyCameraRib.prefab as your camera, anywhere in the ground or behind a character controller.
It contains all the cameras of a cubemap that will be rendered by the Controller into the Fisheye image.

Drop FulldomeCamera/Prefabs/BlendyFisheye3.prefab anywhere.
In it, you can set the BlendyController parameters to configure your output image, like the Horizon and the output Syphon Resolution.
The fisheye image will be rendered and via Syphon via the Funnel plugin, becoming available to any Syphon compatible application, like Blendy Dome VJ, that can be used to output it to the dome.
Syphon works on Mac only, so remove the Funnel component on windows, and try a NDI or Spout plugin instead.

This is an old solution created in Unity 5.4 that's just sitting on my drive, so I'm releasing it as is. There's a simpler implementation based on this article using Unity 2018.1 API: FulldomeCameraForUnity
The plugin will render multiple cameras to compose one Fisheye image, so the game performance can easily become very heavy.
I suggest to create a new Aspect on the Game View called Fulldome, Aspect Ratio of 1:1.
There are two minimal examples FulldomeCamera/Examples/DemoFisheye.scene and FulldomeCamera/Examples/LiveExample.scene.
Fulldome cameras can be placed on the ground or above a player controller. In the LiveExample, the camera is on the ground, but can be easily moved inside the 3rd Person Controller to follow the player, then move it a bit higher and rotate towards the ground to have a 3rd person view.