I've never taken Cloud of Daggers before as I assumed that it occupied only one space on a grid, but after looking into the text of the spell, various passages in the PHB and DMG, and questions others have asked about it online I've come to an alternative interpretation I'm fairly confident in and would like tested.
The text of Cloud of Daggers states that it is 1) a cube 5 feet on each side, and 2) centered on a point.
According to the PHB, a cube's point of origin lies on the face of a cube and is not included in the cube's area of effect. The text for Cloud of Daggers contradicts this by stating that the spell's effect has a point as its center. The DMG defines a point (when using a grid map) as an intersection of squares. This leads to me believe that, using a square grid map, Cloud of Daggers would be centered on the intersection in the middle of four squares. This would mean that Cloud of Daggers would only cover 1/4 of each square; however, according to Jeremy Crawford a target is affected if any of their space is an AoE (with spheres being an exception).
Compare all this with other spells that generate 5-foot cubes. The cantrip Create Bonfire has a description that says the effect fills a 5-foot cube on the ground, but does not specifiy that it is centered on a point. The 2nd-level spell Flaming Sphere has a description that states that a 5-foot diamater sphere appears in an unoccupied space, meaning that it cannot appear on a point.
With all this in mind, my interpretation now is that Cloud of Daggers is supposed to be an AoE that can affect four squares but also does not fill them. I'm not certain exactly why the spell would be written this way rather than specifying a 10-foot cube or an effect with a 5-foot radius centered on a point.
Personally, I'm also inclined to rule that Cloud of Dagger's AoE not covering entire spaces means that creatures could squeeze past unharmed but would be hurt if they walk into it normally or are forced into the area. No other AoE spell is built with a means to squeeze past it, but no other AoE spell is described as a cube centered on a point (as far as I'm aware).
In grid play, Cloud of Daggers can affect 1-4 squares as you choose an intersection of squares as the point of origin of a cube, which lies anywhere on a face of the cubic effect as per the rules. A creature is affected by an effect if any of it's space is included in AoE.
Assuming the specific description in Cloud Of Daggers overrides the general area of effect rules in the PHB, then yes by using the Template method described in Xanathar's up to 4 grid squares could be affected.
However if you instead use the Token method (Also described in Xanathar's) then only 1 5ft square will ever be affected.
As for why not describe the size of the AoE as bigger of it was intended to affect 4 squares? Well, first off then it could affect even more squares. Second, not everyone plays using a gridded map. Some groups might play on a map without gridlines using templates and rulers, other groups might play entirely in theater of the mind. In either case Cloud Of Daggers only ever affects a 5ft cube.
Using 5-foot squares, does cloud of daggers affect a single square? Cloud of daggers (5 ft. cube) can affect more than one square on a grid, unless the DM says effects snap to the grid. There are many ways to position that cube
As I understand it, at least half of a space must be covered by a spell’s effect for the space to be affected, therefore cloud of daggers can at best affect two spaces side by side, or above and below. If it were placed so as to overlap four spaces, in a 3D environment only ⅛ of each space would be covered by the spell’s effect, and therefore technically none of them would be affected as not enough of the spaces are covered.
In grid play, Cloud of Daggers can affect 1-4 squares as you choose an intersection of squares as the point of origin of a cube, which lies anywhere on a face of the cubic effect as per the rules. A creature is affected by an effect if any of it's space is included in AoE.
Assuming the specific description in Cloud Of Daggers overrides the general area of effect rules in the PHB, then yes by using the Template method described in Xanathar's up to 4 grid squares could be affected.
However if you instead use the Token method (Also described in Xanathar's) then only 1 5ft square will ever be affected.
As for why not describe the size of the AoE as bigger of it was intended to affect 4 squares? Well, first off then it could affect even more squares. Second, not everyone plays using a gridded map. Some groups might play on a map without gridlines using templates and rulers, other groups might play entirely in theater of the mind. In either case Cloud Of Daggers only ever affects a 5ft cube.
Also per Sage Advice Compendium;
As I understand it, at least half of a space must be covered by a spell’s effect for the space to be affected, therefore cloud of daggers can at best affect two spaces side by side, or above and below. If it were placed so as to overlap four spaces, in a 3D environment only ⅛ of each space would be covered by the spell’s effect, and therefore technically none of them would be affected as not enough of the spaces are covered.
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