How does orienting a cube-shaped spell work in three-dimensional space?

Question

Can the caster orient the cube any way they like? Can the point of origin effectively be a corner, with the opposite corner pointing any way the caster chooses?

This question was tagged as a duplicate; however, the linked question and its answers presuppose that the cube has a face parallel to the ground. In that question, the "cube" is effectively a square on the ground, plus L feet of airspace above the square (where L is the length of a side of the square).

This question challenges that assumption. I read the rules, and I took them to mean that a cube-shaped spell was an invitation for creative use of three-dimensional geometry.

I get that some groups will ignore or fail to notice this invitation (not every group will enjoy geeking out over geometry). My question, though, is whether this creativity is actually prohibited by the rules. Is there a rules-based argument to prevent, for example,a cube-shaped spell from hitting a target R + L*sqrt(3) feet away, where R is the spell's listed range and L is the listed length of the cube's side?

The description of a cubic area of effect is given as follows (PHB. 204, or here in the basic rules)

CUBE

You select a cube's point of origin, which lies anywhere on a face of the cubic effect. The cube's size is expressed as the length of each side.

A cube's point of origin is not included in the cube's area of effect, unless you decide otherwise.

Can the cube's point of origin be at the corner or edge of the cube-- or at least arbitrarily close to the corner or edge of the cube? Even if we parse "face" as "not including edges or corners," surely the caster can declare that the point of origin is a picometer from the edge or corner?

Can the caster orient the cube at funny angles? I don't see any rule saying the cube can or can't have whatever orientation the caster likes.

Take thunderwave (PHB p. 282) as an example:

A wave of thunderous force sweeps out from you. Each creature in a 15-foot cube originating from you must make a Constitution saving throw. On a failed save, [things happen].

How close does a caster have to get to a single target to hit them with thunderwave? The way I figure it, a caster can set one corner of the cube as the point of origin, then orient the opposite corner in the direction of the intended target.

If I did the math right, the distance across the diagonal of a cube is L*sqrt(3), where L is the length of a side of the cube. Hence, thunderwave could hit a creature as far as 25.98 ft from the caster (because 15ft * sqrt(3) is approximately 25.98 ft).

This would cause part of the spell's Area of Effect (actually, it's a volume) to be blocked by the ground.

Answer 1

This can get surprisingly complicated.

So the first point is, you don't need to use any grid at all. In that case, rotating the cube is natural and you are right with the \$L\sqrt 3\$ diagonal case.

If you do use the grid however, it gets muddy. Dnd measures distances not in normal way, but just as a maximum of coordinates (this is a weird way of saying that diagonal movement costs the same as non-diagonal).

So either you sort of rotate the grid temporarily (in your head) to figure out the area of effect, in which case it works the same as the fist case, even though now you distance from the target is only \$L\$.

Or the grid stays and then you start studying the theory of metric spaces to figure out how does a cube in this situation even look like. The easiest to imagine would be the 45° rotation (2D) case, in which (C- caster, T-Target):

   X
  XXX  
CXXXXT
  XXX
   X

Or to be more srict with the rules about origin and faces (the caster is by the south-west face facing towards north-east):

   X
  XXX  
 XXXXT
C XXX
   X

Notice how the diagonal is 5 squares (or 25 feet) long, while the side is 3. But this feels a bit cheatsy since the concept of cube here is not very well defined.

Finally, note that DMG p.249 has rules/guidelines on how many targets does each shape "usually" hit for theater-of-mind and similar approaches. For Cube it states size/5 (round up), so 15 ft cube gives you around 3 affected targets (in situations where exact positioning is not a top priority).

Answer 2

As you’ve pointed out the Players Handbook (pg 204) states that:

You select a cube's point of origin, which lies anywhere on a face of the cubic effect.The cube's size is expressed as the length of each side.

The edges and corners are part of the face of a cube. As a result there is nothing in the rules preventing you from orienting the cube in any manner you wish.

Xanathar’s Guide to Everything provides rules DMs can use to adjudicate situations like this where you have partially covered squares (on page 86).

The template method is make a template of the shape you want, and then apply this methodology

To use an area-of-effect template, if the terrain is flat, you can lay it on the surface; otherwise, hold the template above the surface and take note of which squares it covers or partially covers. If any part of a square is under the template, the square is included in the area of effect. If a creature is in an affected square, that creature is in the area. Being adjacent to the edge of the template isn’t enough for a square to be included in the area of effect. The square must be entirely or partly covered by the template.

You can also use this method without a grid. If you do so, a creature is included in an area of effect if any part of the miniature's base is overlapped by the template.

Normally the method suggests using 2d templates. Since you want to rotate the shape in 3 dimensions, you will need to create a 3 dimensional template to generate the shadow.

Once you have done that however you can use it in any orientation you choose to generate the shadow.

If you use this method then the furthest distance that you would be able to reach is floor(L*sqrt(3),5) + 5. This is because the template method counts any square that is partly in the shadow of the template to be in the area, so we need to round down to the nearest 5 feet, and then add on 5 feet.

In the case of a 15ft cube this is floor(15*sqrt(3),5) + 5 = floor(25.98,5) + 5 = 30 feet.

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Another way to think about it is, a normally-oriented x-ft cube, where x is some multiple of 5, has (x/5)^3 “5ft cubes of space” that it can effect. It just so happens that 2/3 * (x/5)^3 of them are in the air. Rotating the cube in the way that is described moves some of those cubes from the air, down to the ground (and under the ground).

Taking the 15ft cube described in the question, this gives us 27 5ft cubes that are in the spells area of effect. This equates to 27 small/medium-sized creatures (18 of which are flying), 108 tiny creatures (72 of which are flying), 8 large creatures (4 of which are flying), 1 huge/gargantuan creature.

By reorienting the cube through 3-d space (as opposed to rotating it parallel to the ground) you give up some (a lot) of those flying spaces to affect more spaces in the plane of the ground. The template method described above is the way the game gives to translate a rotation of the 3-d object into a 2-d plane.