Spider familiar climbs on top of cave roof and fires Dragons Breath down upon a group of unsuspecting drow at camp. The cone is a 15Ft spread, which equals 3 tiles horizontal. But from that vantage above it becomes a 9 tile area. of effect The GM allowed it this once for creativity, and the the horror of a tiny spider belching out holy hell from a stalactite onto a spider worshiping race. I was wondering if there were any rules for this sort of use?
It also brought up a bunch of after game discussion about having a hovering familiar breathing down little blasts during a battle, or a shoulder lizard spewing out from under a protected spot on a suit of full plate like the shoulder laser on an Predator.
How many rules are we breaking here?
Rollback Post to RevisionRollBack
IMHO, Earthdawn is still the best fantasy realm, Shadowrun is the best Sci-Fi realm, and Dark Sun is the best D&D realm.
The Area of Effect rules don't really distinguish between three-dimensional cones and two-dimensional ones; your mileage with a DM probably depends on whether "width" is the same concept as "depth" (or "height") . The spell text of some spells like Dragon's Breath are at least neutral towards the question of whether the effect is three-dimensional, but do note that certain other spells like Burning Hands specify that the cone is a "thin sheet", which would suggest that you would get a 3x1 line when fired straight down, not a 3x3 square.
My take as a DM would be to allow three-dimensional cones as the default, but to treat any specific spell text like in Burning Hands that suggests two-dimensional cones to supersede that as a specific exception.
RAW cones are always... Well, cones. Never 2-dimensional fans, no matter what the spell is.
Cone
A cone extends in a direction you choose from its point of origin. A cone's width at a given point along its length is equal to that point's distance from the point of origin. A cone's area of effect specifies its maximum length.
A cone's point of origin is not included in the cone's area of effect, unless you decide otherwise.
Burning hands is actually specifically called out in this section of the rules. It acts the same.
The lack of distinction between a 3D cone and a 2D cone is because there’s no such thing as a 2D cone. No definition, mathematical or vernacular, would say that a cone doesn’t have a (roughly) circular base.
The specific spell text in Burning Hands isn’t a mechanic and doesn’t change the definition of a cone. It’s up the player or DM how to rationalize a “thin sheet” actually affecting a cone AoE, but it’s still a cone AoE. From the PHB, “A cone's width at a given point along its length is equal to that point's distance from the point of origin.” That width is in both dimensions of the cross-sectional area because that’s what a cone is.
Burning hands speaks about the effect starting as "a thin sheet of flames shoots forth from your outstretched fingertips", which I always pictured as the flames beginning as a thin sheet of flames then expanding out to form a cone.
Or...the editor just slipped and did not consider the implications of calling a 'thin sheet of flames extending out on a 2-dimensional plane' a cone to a bunch of gamers who are into minutia and detail, ha-ha.
Rollback Post to RevisionRollBack
IMHO, Earthdawn is still the best fantasy realm, Shadowrun is the best Sci-Fi realm, and Dark Sun is the best D&D realm.
Cones really are something that should be eyeballed and given an estimate (in favor of the player) rather than trying to exactly determine what space they're covering.
Actually mapping them out can get a bit messy. As stated, the width at a certain point along the cone equals its length at that point. This means that in the space in front of you, it's 5 feet wide. Two spaces ahead (10 ft), it's 10 feet wide. Obviously 10 feet is two squares, while a player fills one square; this means that it doesn't cone out from you equally. The next space will be 15 feet wide; now have to decide how it actually widens compared to the space before. If the right side of the cone was directly ahead of the player, do you build the 3rd row so that the player is in the middle of it, or keep the player in line with the right side so the cone now stretches out two spaces to the left of the players space at that point? Note that it can do either, and it's really up to the player.
Look below at the top left picture. Actually trying to translate this into the third dimension is tricky, though if you are a big stickler for making sure everything is exact it is doable. You basically just need to picture that pile of dice vertical as well as horizontal. The thing is, players can aim their cones however they want. Typically it's probably assumed they aimed it straight ahead (and thus almost half of it is hitting the ground) but they can aim it up so the bottom of the cone more or less skirts the ground, and thus the "base" of a 30 ft cone would reach 30 feet up into the air.
"Cones. A cone is represented by rows of tokens on the grid, extending from the cone’s point of origin. In the rows, the squares are adjoining side by side or corner to corner, as shown in diagram 2.5. To determine the number of rows a cone contains, divide its length by 5. For example, a 30-foot cone contains six rows.
Here’s how to create the rows. Starting with a square adjacent to the cone’s point of origin, place one token. The square can be orthogonally or diagonally adjacent to the point of origin. In every row beyond that one, place as many tokens as you placed in the previous row, plus one more token. Place this row’s tokens so that their squares each share a side with a square in the previous row. If the cone is orthogonally adjacent to the point of origin, you’ll have one more token to place in the row; place it on one end or the other of the row you just created (you don’t have to pick the side chosen in diagram 2.5). Keep placing tokens in this way until you’ve created all of the cone’s rows."
Bottom line, you're better off eyeballing it. Just always lean in favor of the player.
The lack of distinction between a 3D cone and a 2D cone is because there’s no such thing as a 2D cone. No definition, mathematical or vernacular, would say that a cone doesn’t have a (roughly) circular base.
The specific spell text in Burning Hands isn’t a mechanic and doesn’t change the definition of a cone. It’s up the player or DM how to rationalize a “thin sheet” actually affecting a cone AoE, but it’s still a cone AoE. From the PHB, “A cone's width at a given point along its length is equal to that point's distance from the point of origin.” That width is in both dimensions of the cross-sectional area because that’s what a cone is.
Not all of a spell's mechanics are found in the spell block, the "Casting a Spell" rules provide that spell text includes spell mechanics: "Each spell description begins with a block of information, including the spell's name, level, school of magic, casting time, range, components, and duration. The rest of a spell entry describes the spell's effect." Spell descriptions are rules text which can and do supercede general rules about spellcasting when applied to that specific spell. See also October 12, 2017 Crawford Tweet , "the descriptions of spells tell you how they work."
Spell text is what permits one to know that Acid Splash can only target creatures, while Fire Bolt can target creatures or objects, or the amount of dice that one rolls. There is no textual support to be found within the rules regarding "the part of the text that is mechanics" and "the part of the text that can be ignored". It isn't surprising that one would find unique mechanics within each spell that aren't worthy of general treatment elsewhere in the rules, Burning Hands creating a "thin sheet" (two-dimensional cone) is one such unique mechanic.
The lack of distinction between a 3D cone and a 2D cone is because there’s no such thing as a 2D cone. No definition, mathematical or vernacular, would say that a cone doesn’t have a (roughly) circular base.
The specific spell text in Burning Hands isn’t a mechanic and doesn’t change the definition of a cone. It’s up the player or DM how to rationalize a “thin sheet” actually affecting a cone AoE, but it’s still a cone AoE. From the PHB, “A cone's width at a given point along its length is equal to that point's distance from the point of origin.” That width is in both dimensions of the cross-sectional area because that’s what a cone is.
The rules do not say that that is "what a cone is," and the Diagram 2.6 draws a two-dimensional cone despite using three-dimensional dice and an isometric view which easily could have been shown creating a three-dimensional effect.
I'm not saying that three-dimensional cones don't make sense. or that conflating "width" with "depth"/"height" isn't a good idea for a DM looking to give his players the benefit of the doubt. I'm just saying, the rules do not specifically state that a cone will always create a three-dimensional effect, and the spell description of certain spells like Burning Handsdo specifically provide mechanics suggesting otherwise.
I wasn’t speaking generally. When I said that the specific text of Burning Hands isn’t a mechanic, I was referencing the same bit of that text that you were and nothing else. I’m not suggesting that you ignore the “thin sheet.” But it doesn’t have any mechanical relevance to the area of effect. The spell text is explicit that everyone in a cone is affected. It is indeed true that the description tells you how the spell works. That’s how we know that Burning Hands affects a cone and not a triangle.
Except the line directly after that says that Burning Hands creates a cone. "As you hold your hands with thumbs touching and fingers spread, a thin sheet of flames shoots forth from your outstretched fingertips. Each creature in a 15-foot cone must make a Dexterity saving throw."
There is no effect in DnD 5e that is a flat fan. Burning Hands is a cone spell, its Range/Area is Self (15 ft Cone). It uses the same Cone rules as all Cones. As I stated, it is even specifically called out in the section of the DMG that covers AoE.
"Spells such as burning hands and cone of cold cover an area, allowing them to affect multiple creatures at once.
A spell's description specifies its area of effect, which typically has one of five different shapes: cone, cube, cylinder, line, or sphere. Every area of effect has a point of origin, a location from which the spell's energy erupts. The rules for each shape specify how you position its point of origin. Typically, a point of origin is a point in space, but some spells have an area whose origin is a creature or an object.
A spell's effect expands in straight lines from the point of origin. If no unblocked straight line extends from the point of origin to a location within the area of effect, that location isn't included in the spell's area. To block one of these imaginary lines, an obstruction must provide total cover, as explained in chapter 9.
Cone
A cone extends in a direction you choose from its point of origin. A cone's width at a given point along its length is equal to that point's distance from the point of origin. A cone's area of effect specifies its maximum length.
A cone's point of origin is not included in the cone's area of effect, unless you decide otherwise."
The flavor text of Burning Hands is just that; flavor text. It says you put your hands out together, but even still you only need 1 free hand to cast it. It says it fires a thin sheet, but its Range/Area is a 15ft Cone.
I wasn’t speaking generally. When I said that the specific text of Burning Hands isn’t a mechanic, I was referencing the same bit of that text that you were and nothing else. I’m not suggesting that you ignore the “thin sheet.” But it doesn’t have any mechanical relevance to the area of effect. The spell text is explicit that everyone in a cone is affected. It is indeed true that the description tells you how the spell works. That’s how we know that Burning Hands affects a cone and not a triangle.
There is no use of the word "triangle" to describe areas of effect that I'm aware of. The diagram used in the rules to describe cones shows and describes a two-dimensional shape drawn on a two-dimensional grid, not a three-dimensional area charted in space. The common real-world understanding of how those shapes interact with space does not preclude them having a different use within the D&D 5E rule system.
Copy Pasta: A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a point called the apex or vertex.
A cone by its very definition cannot be 2-dimensional, and in 5e its width (all around) at a given point is equal to its length from the point of origin, no matter what. Also there is no "depth/height" for a cone, as it has two surfaces it has two measurable dimensions; length and width. You can call them height and depth, but it's the same thing.
Jaysburn, before I go further, I can't remember where diagram 2.6 is that you posted... is that from the same Areas of Effect section and dndbeyond just didn't post the diagram, or was it from a different section?
I will say that unless you also treat Cubes(Thunderwave), Spheres (Darkness), and Cylinders (Moonbeam) as 2-dimensional effects (which you shouldn't), you shouldn't treat Cones as them either. Also Lines (Lightning Bolt), but they're rarely wider than 5 feet.
If they weren't meant to be 3-dimensional, they would be called Circles, Squares, Triangles, etc. And there wouldn't be a difference between Spheres and Cylinders.
Cylinders are specifically described in the Spellcasting rules as having both a radius and a height, so certainly they are not 2-dimensional. I agree that Cubes, Spheres, and yesalso Cones should generally be assumed to be three-dimensional as well, so as not to hold ambiguity against the player. But Cubes, Spheres, and Cones do not include they same explicit reference to a "height" that Cylinders do, and if a spell's description were to give me a specific reason to believe it is a two-dimensional plane of effect (as Burning Hands does), I would trust the spell description and treat it that way notwithstanding the more common three-dimensional significance of the term.
Cubes mention the "length of each side," but not their heights. If one were to describe a square or a rectangle, one would also describe it as defined by the "length of each side." Reading all of the areas of effect together, those rules use "length," "width," "height," and "radius," so they certainly could have mentioned "length and height of each side" if they had meant that. See the wall spells, such as Wall of Light, for language that explicitly describes a three-dimensional shape by using length height and thickness.
Actually, I just stumbled across Entangle and it is interesting. The section on Areas of Effect specifies that "typically" there are five types of area of effect: "typically has one of five different shapes: cone, cube, cylinder, line, or sphere." However, Entangle specifies that it targets a "square," and dndbeyond is so on top of things that the area of effect icon is even a little 2D square instead of the normal 3D cube! Nice! But they don't catch them all, Spike Growth uses the "sphere" icon despite not mentioning the word "sphere" in the spell description, and it is more accurately a flat two-dimensional circle drawn with a 20' radius. One way to interpret this is, if a spell is intended to have a 2D area of effect, the writers can and will come up with a term for a 2d area of effect that isn't one of the five "typical" three dimensional shapes? If Entangle can effect a "square," surely Burning Hands could have effected a "triangle" if that's what was intended? Hmmm.
Then again, there's examples of spells whose description directly contradicts and supersedes the general definitions for their range or area of effect. Etherealness is a good one: its range is "self." Range: Self is defined in the rules as "Other spells, such as the shield spell, affect only you. These spells have a range of self." And yet the description of the spell includes "When you cast this spell using a spell slot of 8th level or higher, you can target up to three willing creatures (including you) for each slot level above 7th. The creatures must be within 10 feet of you when you cast the spell." Note, it does not say "When you cast this spell using a spell slot of 8th level or higher, the range becomes 10 ft.," which is what you would expect if defined ranges/areas of effect can't have their rules broken by spell descriptions. Instead, the range remains "self," but "self" takes on the meaning "up to three willing creatures (including you) within 10 feet of you when you cast the spell."
There are doubtless countless examples of this to be found, but I don't have time to troll through the spell descriptions and find everyone relevant for or against the point I'm trying to make. Instead, here are some Sage Advice tweets that seem at least a little relevant:
July 27, 2015 (Mike Mearls): Best way to map a cone? Cut out a (two-dimensional) cone shape and overlay it on the grid.
December 3, 2015 (Jeremy Crawford): Even though a 5x5' cube would fit within a five-foot square, Crawford seems to think there are ways to position it to be effect more squares because the rules don't require areas of effect to snap to grids. Relevance being... I'm not really sure, that maybe the Area of Effect descriptions aren't the be-all-end-all of what squares are effected?
August 15, 2016 (Mike Mearls): Important point is, when counting width diagonally (or at a crazy angle), don't count width using the movement rules, just overlay a template shape and see what it touches.
August 22, 2016 (Mike Mearls): Cones can originate from points in some pretty novel ways, don't have to be orthogonal or diagonal. Same thing on January 29, 2016 (Jeremy Crawford), best practice continues to be to "place" a 2-dimensional cone shape template.
July 21, 2016 (Mike Mearls): Mike prefers a three-dimensional Cone, but implies that could be a Theater of the Mind vs Grid & Minis play style difference.
September 8, 2016 (Jeremy Crawford): Spheres are an "exception" to the premise that "You can target someone if any of their space is in the AoE." Not sure what "exception" he's referring to, I don't have a physical book handy, not sure what is on Page 251 of DMG that he's referring to???
October 12, 2017 (Jeremy Crawford): Quoted earlier. Look to spell descriptions to figure out how they work, they aren't "fluff" as has been claimed in this thread.
November 27, 2017 (Jeremy Crawford): The XGTE area of effect methods are alternate rules for quicker gameplay, not RAW for the basic rules for the five typical areas of effect.
July 21, 2019 (Dan Dillon): a dragon's breath weapon is indeed a three-dimensional cone which creates a "circle with a diameter" equal to the length of the cone. (So note, OP's 3x3 area of effect wasn't quite right according to Dillon, should probably overlay a 3" diameter circle template over the grid to determine squares effected).
What they are recommending is to do the thing in the top picture here:
Which is by far the easiest way to track the AoE when playing on a grid. But Cones are still a 3D construct. DnD is typically played on a flat surface, but there's times when it's not; in those times you treat Cones as what they are: Cones.
The PHB includes these diagrams for area of effect:
It shows that a cone is a 3D area of effect. The "width" of a cone is synonymous with the diameter of the circle. This is the RAW area of effect for every cone spell (the rules even specifically call out burning hands and cone of cold as working the same way).
Here is the set up.
Spider familiar climbs on top of cave roof and fires Dragons Breath down upon a group of unsuspecting drow at camp. The cone is a 15Ft spread, which equals 3 tiles horizontal. But from that vantage above it becomes a 9 tile area. of effect The GM allowed it this once for creativity, and the the horror of a tiny spider belching out holy hell from a stalactite onto a spider worshiping race. I was wondering if there were any rules for this sort of use?
It also brought up a bunch of after game discussion about having a hovering familiar breathing down little blasts during a battle, or a shoulder lizard spewing out from under a protected spot on a suit of full plate like the shoulder laser on an Predator.
How many rules are we breaking here?
IMHO, Earthdawn is still the best fantasy realm, Shadowrun is the best Sci-Fi realm, and Dark Sun is the best D&D realm.
You are not breaking any rules (as there are very few that address verticality or climbing on creatures).
At the very least, a climbing or flying familiar firing a dragon breath down in a circular area of effect is entirely RAW.
The sholder lizard that shares armor is a bit greyer and will require DM permission.
We were just thinking of really goofy ways of hiding a familiar so they would be harder to immediately targeted by any sort of intelligent enemy.
IMHO, Earthdawn is still the best fantasy realm, Shadowrun is the best Sci-Fi realm, and Dark Sun is the best D&D realm.
The Area of Effect rules don't really distinguish between three-dimensional cones and two-dimensional ones; your mileage with a DM probably depends on whether "width" is the same concept as "depth" (or "height") . The spell text of some spells like Dragon's Breath are at least neutral towards the question of whether the effect is three-dimensional, but do note that certain other spells like Burning Hands specify that the cone is a "thin sheet", which would suggest that you would get a 3x1 line when fired straight down, not a 3x3 square.
My take as a DM would be to allow three-dimensional cones as the default, but to treat any specific spell text like in Burning Hands that suggests two-dimensional cones to supersede that as a specific exception.
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RAW cones are always... Well, cones. Never 2-dimensional fans, no matter what the spell is.
Cone
A cone extends in a direction you choose from its point of origin. A cone's width at a given point along its length is equal to that point's distance from the point of origin. A cone's area of effect specifies its maximum length.
A cone's point of origin is not included in the cone's area of effect, unless you decide otherwise.
Burning hands is actually specifically called out in this section of the rules. It acts the same.
The lack of distinction between a 3D cone and a 2D cone is because there’s no such thing as a 2D cone. No definition, mathematical or vernacular, would say that a cone doesn’t have a (roughly) circular base.
The specific spell text in Burning Hands isn’t a mechanic and doesn’t change the definition of a cone. It’s up the player or DM how to rationalize a “thin sheet” actually affecting a cone AoE, but it’s still a cone AoE. From the PHB, “A cone's width at a given point along its length is equal to that point's distance from the point of origin.” That width is in both dimensions of the cross-sectional area because that’s what a cone is.
Burning hands speaks about the effect starting as "a thin sheet of flames shoots forth from your outstretched fingertips", which I always pictured as the flames beginning as a thin sheet of flames then expanding out to form a cone.
Or...the editor just slipped and did not consider the implications of calling a 'thin sheet of flames extending out on a 2-dimensional plane' a cone to a bunch of gamers who are into minutia and detail, ha-ha.
IMHO, Earthdawn is still the best fantasy realm, Shadowrun is the best Sci-Fi realm, and Dark Sun is the best D&D realm.
Cones really are something that should be eyeballed and given an estimate (in favor of the player) rather than trying to exactly determine what space they're covering.
Actually mapping them out can get a bit messy. As stated, the width at a certain point along the cone equals its length at that point. This means that in the space in front of you, it's 5 feet wide. Two spaces ahead (10 ft), it's 10 feet wide. Obviously 10 feet is two squares, while a player fills one square; this means that it doesn't cone out from you equally. The next space will be 15 feet wide; now have to decide how it actually widens compared to the space before. If the right side of the cone was directly ahead of the player, do you build the 3rd row so that the player is in the middle of it, or keep the player in line with the right side so the cone now stretches out two spaces to the left of the players space at that point? Note that it can do either, and it's really up to the player.
Look below at the top left picture. Actually trying to translate this into the third dimension is tricky, though if you are a big stickler for making sure everything is exact it is doable. You basically just need to picture that pile of dice vertical as well as horizontal. The thing is, players can aim their cones however they want. Typically it's probably assumed they aimed it straight ahead (and thus almost half of it is hitting the ground) but they can aim it up so the bottom of the cone more or less skirts the ground, and thus the "base" of a 30 ft cone would reach 30 feet up into the air.
"Cones. A cone is represented by rows of tokens on the grid, extending from the cone’s point of origin. In the rows, the squares are adjoining side by side or corner to corner, as shown in diagram 2.5. To determine the number of rows a cone contains, divide its length by 5. For example, a 30-foot cone contains six rows.
Here’s how to create the rows. Starting with a square adjacent to the cone’s point of origin, place one token. The square can be orthogonally or diagonally adjacent to the point of origin. In every row beyond that one, place as many tokens as you placed in the previous row, plus one more token. Place this row’s tokens so that their squares each share a side with a square in the previous row. If the cone is orthogonally adjacent to the point of origin, you’ll have one more token to place in the row; place it on one end or the other of the row you just created (you don’t have to pick the side chosen in diagram 2.5). Keep placing tokens in this way until you’ve created all of the cone’s rows."
Bottom line, you're better off eyeballing it. Just always lean in favor of the player.
Not all of a spell's mechanics are found in the spell block, the "Casting a Spell" rules provide that spell text includes spell mechanics: "Each spell description begins with a block of information, including the spell's name, level, school of magic, casting time, range, components, and duration. The rest of a spell entry describes the spell's effect." Spell descriptions are rules text which can and do supercede general rules about spellcasting when applied to that specific spell. See also October 12, 2017 Crawford Tweet , "the descriptions of spells tell you how they work."
Spell text is what permits one to know that Acid Splash can only target creatures, while Fire Bolt can target creatures or objects, or the amount of dice that one rolls. There is no textual support to be found within the rules regarding "the part of the text that is mechanics" and "the part of the text that can be ignored". It isn't surprising that one would find unique mechanics within each spell that aren't worthy of general treatment elsewhere in the rules, Burning Hands creating a "thin sheet" (two-dimensional cone) is one such unique mechanic.
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The rules do not say that that is "what a cone is," and the Diagram 2.6 draws a two-dimensional cone despite using three-dimensional dice and an isometric view which easily could have been shown creating a three-dimensional effect.
I'm not saying that three-dimensional cones don't make sense. or that conflating "width" with "depth"/"height" isn't a good idea for a DM looking to give his players the benefit of the doubt. I'm just saying, the rules do not specifically state that a cone will always create a three-dimensional effect, and the spell description of certain spells like Burning Hands do specifically provide mechanics suggesting otherwise.
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I'm going to make this way harder than it needs to be.
I wasn’t speaking generally. When I said that the specific text of Burning Hands isn’t a mechanic, I was referencing the same bit of that text that you were and nothing else. I’m not suggesting that you ignore the “thin sheet.” But it doesn’t have any mechanical relevance to the area of effect. The spell text is explicit that everyone in a cone is affected. It is indeed true that the description tells you how the spell works. That’s how we know that Burning Hands affects a cone and not a triangle.
Except the line directly after that says that Burning Hands creates a cone. "As you hold your hands with thumbs touching and fingers spread, a thin sheet of flames shoots forth from your outstretched fingertips. Each creature in a 15-foot cone must make a Dexterity saving throw."
There is no effect in DnD 5e that is a flat fan. Burning Hands is a cone spell, its Range/Area is Self (15 ft Cone). It uses the same Cone rules as all Cones. As I stated, it is even specifically called out in the section of the DMG that covers AoE.
"Spells such as burning hands and cone of cold cover an area, allowing them to affect multiple creatures at once.
A spell's description specifies its area of effect, which typically has one of five different shapes: cone, cube, cylinder, line, or sphere. Every area of effect has a point of origin, a location from which the spell's energy erupts. The rules for each shape specify how you position its point of origin. Typically, a point of origin is a point in space, but some spells have an area whose origin is a creature or an object.
A spell's effect expands in straight lines from the point of origin. If no unblocked straight line extends from the point of origin to a location within the area of effect, that location isn't included in the spell's area. To block one of these imaginary lines, an obstruction must provide total cover, as explained in chapter 9.
Cone
A cone extends in a direction you choose from its point of origin. A cone's width at a given point along its length is equal to that point's distance from the point of origin. A cone's area of effect specifies its maximum length.
A cone's point of origin is not included in the cone's area of effect, unless you decide otherwise."
The flavor text of Burning Hands is just that; flavor text. It says you put your hands out together, but even still you only need 1 free hand to cast it. It says it fires a thin sheet, but its Range/Area is a 15ft Cone.
There is no use of the word "triangle" to describe areas of effect that I'm aware of. The diagram used in the rules to describe cones shows and describes a two-dimensional shape drawn on a two-dimensional grid, not a three-dimensional area charted in space. The common real-world understanding of how those shapes interact with space does not preclude them having a different use within the D&D 5E rule system.
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Copy Pasta: A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a point called the apex or vertex.
A cone by its very definition cannot be 2-dimensional, and in 5e its width (all around) at a given point is equal to its length from the point of origin, no matter what. Also there is no "depth/height" for a cone, as it has two surfaces it has two measurable dimensions; length and width. You can call them height and depth, but it's the same thing.
Jaysburn, before I go further, I can't remember where diagram 2.6 is that you posted... is that from the same Areas of Effect section and dndbeyond just didn't post the diagram, or was it from a different section?
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I'm going to make this way harder than it needs to be.
That one is in Xanathar's Guide to Everything.
They could have shown it vertically too, as you say, but it would be near impossible to tell what is actually happening in that case.
I will say that unless you also treat Cubes(Thunderwave), Spheres (Darkness), and Cylinders (Moonbeam) as 2-dimensional effects (which you shouldn't), you shouldn't treat Cones as them either. Also Lines (Lightning Bolt), but they're rarely wider than 5 feet.
If they weren't meant to be 3-dimensional, they would be called Circles, Squares, Triangles, etc. And there wouldn't be a difference between Spheres and Cylinders.
Cylinders are specifically described in the Spellcasting rules as having both a radius and a height, so certainly they are not 2-dimensional. I agree that Cubes, Spheres, and yes also Cones should generally be assumed to be three-dimensional as well, so as not to hold ambiguity against the player. But Cubes, Spheres, and Cones do not include they same explicit reference to a "height" that Cylinders do, and if a spell's description were to give me a specific reason to believe it is a two-dimensional plane of effect (as Burning Hands does), I would trust the spell description and treat it that way notwithstanding the more common three-dimensional significance of the term.
Cubes mention the "length of each side," but not their heights. If one were to describe a square or a rectangle, one would also describe it as defined by the "length of each side." Reading all of the areas of effect together, those rules use "length," "width," "height," and "radius," so they certainly could have mentioned "length and height of each side" if they had meant that. See the wall spells, such as Wall of Light, for language that explicitly describes a three-dimensional shape by using length height and thickness.
Actually, I just stumbled across Entangle and it is interesting. The section on Areas of Effect specifies that "typically" there are five types of area of effect: "typically has one of five different shapes: cone, cube, cylinder, line, or sphere." However, Entangle specifies that it targets a "square," and dndbeyond is so on top of things that the area of effect icon is even a little 2D square instead of the normal 3D cube! Nice! But they don't catch them all, Spike Growth uses the "sphere" icon despite not mentioning the word "sphere" in the spell description, and it is more accurately a flat two-dimensional circle drawn with a 20' radius. One way to interpret this is, if a spell is intended to have a 2D area of effect, the writers can and will come up with a term for a 2d area of effect that isn't one of the five "typical" three dimensional shapes? If Entangle can effect a "square," surely Burning Hands could have effected a "triangle" if that's what was intended? Hmmm.
Then again, there's examples of spells whose description directly contradicts and supersedes the general definitions for their range or area of effect. Etherealness is a good one: its range is "self." Range: Self is defined in the rules as "Other spells, such as the shield spell, affect only you. These spells have a range of self." And yet the description of the spell includes "When you cast this spell using a spell slot of 8th level or higher, you can target up to three willing creatures (including you) for each slot level above 7th. The creatures must be within 10 feet of you when you cast the spell." Note, it does not say "When you cast this spell using a spell slot of 8th level or higher, the range becomes 10 ft.," which is what you would expect if defined ranges/areas of effect can't have their rules broken by spell descriptions. Instead, the range remains "self," but "self" takes on the meaning "up to three willing creatures (including you) within 10 feet of you when you cast the spell."
There are doubtless countless examples of this to be found, but I don't have time to troll through the spell descriptions and find everyone relevant for or against the point I'm trying to make. Instead, here are some Sage Advice tweets that seem at least a little relevant:
July 27, 2015 (Mike Mearls): Best way to map a cone? Cut out a (two-dimensional) cone shape and overlay it on the grid.
December 3, 2015 (Jeremy Crawford): Even though a 5x5' cube would fit within a five-foot square, Crawford seems to think there are ways to position it to be effect more squares because the rules don't require areas of effect to snap to grids. Relevance being... I'm not really sure, that maybe the Area of Effect descriptions aren't the be-all-end-all of what squares are effected?
August 15, 2016 (Mike Mearls): Important point is, when counting width diagonally (or at a crazy angle), don't count width using the movement rules, just overlay a template shape and see what it touches.
August 22, 2016 (Mike Mearls): Cones can originate from points in some pretty novel ways, don't have to be orthogonal or diagonal. Same thing on January 29, 2016 (Jeremy Crawford), best practice continues to be to "place" a 2-dimensional cone shape template.
July 21, 2016 (Mike Mearls): Mike prefers a three-dimensional Cone, but implies that could be a Theater of the Mind vs Grid & Minis play style difference.
September 8, 2016 (Jeremy Crawford): Spheres are an "exception" to the premise that "You can target someone if any of their space is in the AoE." Not sure what "exception" he's referring to, I don't have a physical book handy, not sure what is on Page 251 of DMG that he's referring to???
October 12, 2017 (Jeremy Crawford): Quoted earlier. Look to spell descriptions to figure out how they work, they aren't "fluff" as has been claimed in this thread.
November 27, 2017 (Jeremy Crawford): The XGTE area of effect methods are alternate rules for quicker gameplay, not RAW for the basic rules for the five typical areas of effect.
July 21, 2019 (Dan Dillon): a dragon's breath weapon is indeed a three-dimensional cone which creates a "circle with a diameter" equal to the length of the cone. (So note, OP's 3x3 area of effect wasn't quite right according to Dillon, should probably overlay a 3" diameter circle template over the grid to determine squares effected).
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I'm going to make this way harder than it needs to be.
What they are recommending is to do the thing in the top picture here:
Which is by far the easiest way to track the AoE when playing on a grid. But Cones are still a 3D construct. DnD is typically played on a flat surface, but there's times when it's not; in those times you treat Cones as what they are: Cones.
The PHB includes these diagrams for area of effect:
It shows that a cone is a 3D area of effect. The "width" of a cone is synonymous with the diameter of the circle. This is the RAW area of effect for every cone spell (the rules even specifically call out burning hands and cone of cold as working the same way).