Polytopia Wiki
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Essentially, a unit's Movement stat determines how many “moves” it has in one turn. (A unit with 0.5 moves remaining will still be able to take a step that requires 1 move.) Movement from “normal” tiles, such as Fields, takes 1 move. Units cannot move through “terminal” tiles. For land units, these are Forests, Mountains, and any adjacent to enemy units. (Climbing needs to be researched before units can move onto Mountains.) Units cannot move into/through the fog of war (clouds). Land units cannot move further after moving onto a Port (which can only be done after Sailing is researched). For Polaris: if Polarism is researched, land units gain 1 extra move when they step onto Ice for the first time.

Roads

Movement between two tiles with Roads (or a Road and a city) requires only 0.5 moves, even if one or both of these tiles are Forests. You can use Roads in neutral territory but not Roads in enemy territory. 

Note that the game often misses “longer” paths that require fewer moves due to Roads, so when using elaborate Road systems for Riders and Knights, make sure you have a backup in case your Roads do not work (usually building more Roads).

Special Movement Types

The units listed below have special movement types. (All other units are land units.) Special movement types are shown in-game with the unit’s skills

  • Carry (Boat, Ship, Battleship): can freely move across water. (To move to Ocean tiles, either Navigation or, for Aquarion, Free Diving must be researched.) Can move onto land, but any land tile is considered terminal. 
    • Note: trade routes over water are not roads! They don’t affect movement for any unit.
  • Swim (Amphibian, Tridention, Crab): same as Carry units, but can also move across land. Can utilize Roads. Without Roads, can only move one tile on land. 
  • Fly (Baby and Fire Dragon): ignore terminal tiles and all other movement barriers (except fog of war and enemy units), but cannot utilize Roads. Cannot examine Ruins.
  • Navigate (Navalon): can only move on water tiles. Consider cities to be water tiles.
  • Skate (Mooni, Battle Sled, Ice Fortress): consider all land tiles to be terminal. Dash and Escape skills cannot be utilized on land. Consider cities as Ice tiles. Cannot utilize Roads (exception: if standing on a Road next to an Ice tile, will be able to move to the Ice tile and continue movement). 
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