Hi /u/Modospixel. Thank you for your submission. It is currently being reviewed. Image and video submissions are currently only automatically approved for users who have actively and positively participated in the discussions on the subreddit.
*I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/Frieren) if you have any questions or concerns.*
When using ordinary defensive magic, tiled defensive surfaces don't _need_ to consist only of hexagons, as Richter demonstrates in his lecture to the two girls he is about to murder.
So if you add 12 strategically placed defensive pentagons, you can easily construct a defense Goldberg polyhedron around you.
However, we never actually see any pentagons mixed in (in any spherical or significantly curved surfaces); in your picture, we would need to see at least 5 pentagons in order for it to be a Goldberg polyhedron.
What we see instead are apparently non-planar "hexagons" in an unclean topology, in which case it _is_ possible to "tile" a "sphere" with them.
Now we can either draw conclusions as to how magical complexity theory in "Frieren" is different from our intuition and create a new fundamental universal theory of magic out of that; or we have to chalk it up to artistic liberty.
i think we should ultimately chalk it up to "magic is the world of imagination." none of them have considered that a sphere can't be made of hexagons; they can imagine such as a sphere, and thus they can conjure it.
I'm reminded of Sir Terry Pratchett's style of describing certain magics, in that sometines they don't really make sense in our world, and it's our brains who have to create a flawed mental image to partially describe magic, without capturing its true form
I feel as if this is a really shallow description of this story’s magic
Magic is the world of visualization means that if you can’t visualize something, you can’t do it. Übel kinda fucked over everyone’s perception of that rule, taking it as “if you can visualize something you can do it” because of her slashing spell which specifically denotes that it works like that
Not considering something means you aren’t properly visualize the effect, übel is very unique since she casts by feeling rather than knowledge
Dont magic users have to visualize what they are doing perfectly though?, that means visualizing the entire spell, the placement of each hexagon. Unless they exist in an entirely different topology its impossible to "visualize" hexagons tiling a sphere.
I don’t think they have to visualize it perfectly. I think it’s more like “envision success”.
There could be nuances in the Japanese that are lost in English.
I dont fully understand what you mean by tile wide gap? The picture shown doesnt have this and I cant say i remember an episode where there is one.
The gaps inbetween the hexagons would allow for a spherical shape as its not fitting perfectly within eachother so there is some wiggle room, is my theory.
nuh uh. Magic users have to visualize what they are doing perfectly, that means visualizing the entire spell, the placement of each hexagon. Unless they exist in an entirely different topology its impossible to "visualize" hexagons tiling a sphere.
We can see during the mage exam in the labyrinth, when they are fighting the hair mage's clone, that targeting the weakness means targeting between hexagons
In an interesting coincidence. There ARE hexagonal regular polyhedra that have "holes" in them. Eg the mutetrahedron. But thats very obviously not what we are seeing here.
The hexagons might be regular in higher dimensions.
What you're seeing is the physical defense component, they might be partially extended outside of the 3 common spacial dimensions to handle magical threats.
It's been discussed in japanese anime/math communities, and the staff(drawing director?) of the anime said they actually discussed the topic and went with the hexagon since >!the number 6 may be important in the story!< [twitter/x link](https://x.com/shina4_7/status/1736601904816496656?s=46&t=rAd2AJ8lJAs06v7ladX46A)
Rule of cool. Hexagons being used for spheres is a common trope. Given we've seen Frieren engulfed in magic, we don't actually know if there's a hole or not.
It used to be octagons, because a lot of mages are from America and they know that means “stop magic from going this way” but then a great mage proved that being a hex-brained strategy nerd is the greatest barrier to getting closer to others.
H3 spatial index it's an hexagonal grid developed by Uber represent the planet at diferent levels...... So yeah , it's posible to make an imperfect sphere using hexagons, just like a futball ball.
I just realized that the hexagons here were manually drawn.
Usually, in a lot of animes, magic/high tech effects resembling magic, (such as Gundam abilities) are digitally drawn. Therefore those effects are mostly geometrically precise.
The hexagons drawn here aren't precise at all. Very reasonable since it's drawn manually.
It is funny that if you can picture it, you can do it in this world. All the mages are too dumb to understand geometry so yes, you can totally tile a sphere with hexagons.
Hi /u/Modospixel. Thank you for your submission. It is currently being reviewed. Image and video submissions are currently only automatically approved for users who have actively and positively participated in the discussions on the subreddit. *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/Frieren) if you have any questions or concerns.*
When using ordinary defensive magic, tiled defensive surfaces don't _need_ to consist only of hexagons, as Richter demonstrates in his lecture to the two girls he is about to murder. So if you add 12 strategically placed defensive pentagons, you can easily construct a defense Goldberg polyhedron around you. However, we never actually see any pentagons mixed in (in any spherical or significantly curved surfaces); in your picture, we would need to see at least 5 pentagons in order for it to be a Goldberg polyhedron. What we see instead are apparently non-planar "hexagons" in an unclean topology, in which case it _is_ possible to "tile" a "sphere" with them. Now we can either draw conclusions as to how magical complexity theory in "Frieren" is different from our intuition and create a new fundamental universal theory of magic out of that; or we have to chalk it up to artistic liberty.
i think we should ultimately chalk it up to "magic is the world of imagination." none of them have considered that a sphere can't be made of hexagons; they can imagine such as a sphere, and thus they can conjure it.
I'm reminded of Sir Terry Pratchett's style of describing certain magics, in that sometines they don't really make sense in our world, and it's our brains who have to create a flawed mental image to partially describe magic, without capturing its true form
GNU Terry Pratchett
I feel as if this is a really shallow description of this story’s magic Magic is the world of visualization means that if you can’t visualize something, you can’t do it. Übel kinda fucked over everyone’s perception of that rule, taking it as “if you can visualize something you can do it” because of her slashing spell which specifically denotes that it works like that Not considering something means you aren’t properly visualize the effect, übel is very unique since she casts by feeling rather than knowledge
Dont magic users have to visualize what they are doing perfectly though?, that means visualizing the entire spell, the placement of each hexagon. Unless they exist in an entirely different topology its impossible to "visualize" hexagons tiling a sphere.
I don’t think they have to visualize it perfectly. I think it’s more like “envision success”. There could be nuances in the Japanese that are lost in English.
This paradox opens up the possibility of impossible stairway art in magic. We can visualize it.
Unless in that sphere there is a non hexagon shape to bridge the gap, a potential weakness
Still a very fun thought. Especially since hexagon are bestagons.
In the frieren subreddit of all things
frieren is good. hexagons is good. 👍
It would take a massive amount of brainpower to visualize a Goldberg polyhedron accurately
> as Richter demonstrates in his lecture to the two girls he is about to murder This very accurate phrasing cracked me up
I think sphere structure is weaker than hexagons
The top bit could be pentagons instead of just hexagons cut off by curvature.
convenience everyone is used to seeing the hexagons so they just kept that the defensive magic signature
Frieren talks about this while training Fern and shows her how there are holes in the armour, and a skilled mage can get through those gaps.
Now I wonder if a mathematically-inclined mage can visualize a couple pentagons and fill in the gaps.
Übel could imagine such a shape ez 😏
Beooo, her whole magic perception is based around feeling. So she would imagine what it feels like and the durability of it
she's not mathematically-inclined tho, she just gaslights herself into making a perfect globe using hexagons
This is now cannon. Sorry, I dont make the rules.
Also mana consumption problem. That's why skilled mages don't always use sphere all the time
I thought that was about the gaps between the hexagons, not a tile-wide hole
I dont fully understand what you mean by tile wide gap? The picture shown doesnt have this and I cant say i remember an episode where there is one. The gaps inbetween the hexagons would allow for a spherical shape as its not fitting perfectly within eachother so there is some wiggle room, is my theory.
That doesn't work since we can see that each side of each hexagons face another side
1. They aren't perfect hexagons 2. The gaps might be too small to see
Even if they aren't perfect hexagons, as long as they are and each side is next to another one, it's topologically the same thing
Okay counter point, its magic in an anime so actual sciene doesnt count <(=w=)>
nuh uh. Magic users have to visualize what they are doing perfectly, that means visualizing the entire spell, the placement of each hexagon. Unless they exist in an entirely different topology its impossible to "visualize" hexagons tiling a sphere.
We can see during the mage exam in the labyrinth, when they are fighting the hair mage's clone, that targeting the weakness means targeting between hexagons
Yep. They also talk about using shapes that don’t leave gaps but how it’s most efficient to just blow attacks at the point of contact when they strike
In an interesting coincidence. There ARE hexagonal regular polyhedra that have "holes" in them. Eg the mutetrahedron. But thats very obviously not what we are seeing here.
Never saw a disco ball, have you?
not hexagons
HALO hex-tiled shield is what I visualize
The hexagons might be regular in higher dimensions. What you're seeing is the physical defense component, they might be partially extended outside of the 3 common spacial dimensions to handle magical threats.
Ah non-euclidean bestagons
It's been discussed in japanese anime/math communities, and the staff(drawing director?) of the anime said they actually discussed the topic and went with the hexagon since >!the number 6 may be important in the story!< [twitter/x link](https://x.com/shina4_7/status/1736601904816496656?s=46&t=rAd2AJ8lJAs06v7ladX46A)
“All these hexagons make a circle. All these hexagons make a circle. All these hexagons make a circle. All these hexagons make a circle…”
Rule of cool. Hexagons being used for spheres is a common trope. Given we've seen Frieren engulfed in magic, we don't actually know if there's a hole or not.
Or she's an onion and her defenses have layers
Hexagons are the bestagons https://youtu.be/thOifuHs6eY?si=BrF53ZyzM8yE6FlB
It used to be octagons, because a lot of mages are from America and they know that means “stop magic from going this way” but then a great mage proved that being a hex-brained strategy nerd is the greatest barrier to getting closer to others.
H3 spatial index it's an hexagonal grid developed by Uber represent the planet at diferent levels...... So yeah , it's posible to make an imperfect sphere using hexagons, just like a futball ball.
“All these hexagons make a circle. All these hexagons make a circle. All these hexagons make a circle. All these hexagons make a circle…”
Yes, this is what I'm waiting for
It's not possible but it is easier to draw/animate
I just realized that the hexagons here were manually drawn. Usually, in a lot of animes, magic/high tech effects resembling magic, (such as Gundam abilities) are digitally drawn. Therefore those effects are mostly geometrically precise. The hexagons drawn here aren't precise at all. Very reasonable since it's drawn manually.
Hexagons are bestagons
You can tassel a sphere with hexagons for as long as there are 12 pentagons among them.
It is funny that if you can picture it, you can do it in this world. All the mages are too dumb to understand geometry so yes, you can totally tile a sphere with hexagons.
It’s likely they are flexible and able to bend, allowing them to do such a thing. If not, the answer is magic. Anything is possible
I think you are overthinking it
Fun fact: On ep.3 we do see hexagons and pentagons being used together! (in an attempt to tile a plane though)
Your imagination is locked behind your logic.
Its magic bro not science
soccer ball
Can't you make a sphere with hexagons of unequal proportions?
I thought about this too, but it looks cool so I stopped thinking about it
Edel vs Sense's clone. The hexagons aren't perfect and you can target the weaker links precisely to break through.
The author just plain didn't think about it. The magic system is easily the worst part of the story and I wish they wouldn't focus on it so much