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)
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.