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I know that in 4E D&D, there is a rule that states creatures are facing 360' at all times. I understand the nature of this when a creature occupies a square 'footprint' ex: 2x2, 4x4. But, when a creature (ex Horse) occupies 2x1 squares, and the rider of the horse is located as part of one of those squares, does the 360' facing still apply?

I am thinking that a rider, who occupies the 'head' section of a horse can not immediately spin his horse to threaten creatures that were previously unthreatened because the horse's "rump" section occupied the square between them.

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No, because creatures don't occupy 1x2 squares

A horse in 4e is a large creature. All large creatures occupy 2x2 squares on the grid map, regardless of their actual dimensions.

Think of the 2x2 squares not as the creature's actual dimensions, but as the amount of space it requires to freely move about the battle grid and defend itself.

Part of this abstraction is that the horse can freely rotate at all times, effectively facing in all directions at once (for purposes of game mechanics).

So far as the rider of the mount is concerned, treat them as though they occupy all of the squares occupied by their mount. If something can hit the mount, it can hit the rider.

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This! Remember squares are 5' cubes. Most people don't entirely fill a 5' cube. Many people couldn't even touch both walls of a 5' cube. –  aslum Mar 7 '12 at 18:06
If a rider "is allowed to be in any square that the horse occupies" (2x2), how does a character get attacked from a opponent with a reach 1 melee weapon? –  Paraic Mulgrew Mar 7 '12 at 19:23
@ParaicMulgrew - the short answer is that it is easier to consider the rider to be the same size as the horse for almost all purposes as this is how the rules work out. The only exception I can think of off hand is that aura's generated by the rider must still come from only 1 square (so an aura 1 is 9 squares total). If you need more detail or rules citations, break this out into a separate question and I or someone else will provide them. –  Pat Ludwig Mar 7 '12 at 19:49

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