The Battle of Polytopia contains two confirmed Easter eggs. There is also the Luxidoor Easter egg, which can not be officially called an Easter egg but can be considered as one.
Nature Bunny EditTap ten times on any unoccupied square in your territory and you will spawn a Nature Bunny. The bunny moves randomly around the map, destroying any unit or building it touches. Nature Bunnies can be destroyed just like any other unit in the game. A Nature Bunny counts as an enemy unit in the sense that if one is on your city, you will not gain resources from it. The Nature Bunny can be used to your advantage if you have an unoccupied square of land that is separated from the land your city is on. It can also be used to remove unwanted buildings.
Sky/Rising Sun Edit
To do this Easter egg, have a unit in your territory at the edge of the world then touch and hold the sky for 20 seconds. Then, the sun will rise over the world. Touching and holding the sky or another 15 seconds will bring back the standard black sky, albeit without stars. Relaunching the app and resuming the game will restore the sky to default.
Luxidoor Easter Egg EditNormally, when you do not own a tribe, you don't get them in your game. The Luxidoor appear every once in a while to players who don't own them. This can be considered an Easter Egg because they are not meant to be in the games. There is no known pattern as to in what settings it happens to your games. The rough percentage of the Luxidoor appearing is 5-10% depending on how many games you play.
Floating/Sinking City Easter Egg Edit
Alternately tap on the bottom left and bottom right tiles of a city. The city will either rise or sink lower. This may be a glitch or intentional Easter Egg. To get the city to float, start by tapping on the bottom left square. To get it to sink, start by tapping on the bottom right square. It will reset after training a unit or hitting the next turn button.