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

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.

• @GregFaust: Re your second point, that is exactly the value proposition for marking questions as duplicates: so folks searching for them but using different terms can find the answers that are already good. – user17995 Jun 15 '18 at 5:31
• I think you should split this into 2 questions: one about where on the side the point of origin can be and another about rotating the area. – Szega Jun 15 '18 at 8:54
• @TuggyNE Ah, so it's not a mark of shame. It's not, "This is a duplicate; you're so silly for not using a search engine." Rather it's, "This is a duplicate; let's save answerers the trouble of drafting a new answer." (Incidentally, I still maintain that this isn't a duplicate, as the other question's answers don't address 3d geometry.) – Greg Faust Jun 15 '18 at 10:22
• @GregFaust its worth noting that its generally the question that marks something as a duplicate, not the fact that they have the same/similar answers – Wibbs Jun 15 '18 at 12:34
• Is your question really about geometry and positioning or about how much of an opponent's space is required in order for it to be affected by the spell? Also, do you use a battlemap or Theatre of the Mind? – NautArch Jun 15 '18 at 13:05

### 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).

• I never thought about the consequences of maximum of coordinates like this! Theoretically turning the cube 45 degrees on a vertical axis would let you target a maximum of 13 creature's spaces instead of the normally aligned 9. Of course, you could use a square form three squares long on each side and measure the size in that way to keep it super fair. I know I reference him a lot, and he's not infallible by any means, but I've seen Matt Mercer of Critical Role do that often... – Isaac Reefman Jun 15 '18 at 7:47
• @IsaacReefman yeah, that just shows how little meaning the term cube has here. Usually you think about it in terms of perpendicularity and lines, but both lines and perpendicularity don't really exist on the grid, only sort of "behind it". – J.E Jun 15 '18 at 8:01
• @IsaacReefman I'm not so sure you could hit 13 creatures instead of 9, unless your DM was feeling generous. I assume we're talking about medium or small creatures, in which case they're each considered to occupy a 5'x5' square (PHB p. 191). I would expect a DM to rule that, if the right and left edges of your spray are halfway-covering some monsters' squares, you need to pick whether you'll try to include the ones on the right or the ones on the left (and that you can't hit both). Of course, I'm assuming that the DM is trying to preserve the spirit of the rule: 15x15 square = 9 targets max. – Greg Faust Jun 15 '18 at 10:09
• honestly, i think that the only practical way of dealing with this sort of stuff is some sort of template or frame, that you would easily apply on your battlefield to see who does fit in and who doesn't. You will still have to solve the issue of when to include partially covered squares, though, and that is always gonna end up on the DM... – J.E Jun 15 '18 at 10:33
• @GregFaust 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. – J.E Jun 17 '18 at 14:07

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.

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.