Non-Euclidean Geography
The map doesn't work here
Ah, non-Euclidean geography, and its kissing cousin, non-Euclidean architecture!
Never mind Gauss -- ignore Lobachevsky -- what you need to consider is Escher.
L. Sprague de Camp, for all his virtues, did complain once that E.R. Eddison once depicted a world inside another world. If you descended to this world, you could find another world inside it. And if you descended to that world, you could find a world inside it -- in fact the original one. He said that you do not know the theory of sets to know that if A contains B and B contains C, C can not contain A.
Faced with such logic, you can only smile broadly and look back to the work, to enjoy it.
If you go straight through the valley of wheat fields to the village and its dock, that will take you all day. If you go around, it will take a couple of hours.
And that would be a highly simple case. Most lead to labyrinthine paths.1
In theory, of course, this can be clearly distinguished from situations where the paths actively move, or the walls, or hedges, or mountains, and also from the situations where magic confuses the traveler's sense of direction so much that Euclidean set-ups don't seem it.
But the very nature of the trope means that the characters (and the reader) may have difficulty finding out which one is in effect. Sometimes the puzzle is finally insoluble. Possibly even more than one trope is, though that is uncommon. (If you don't have a good explanation for why even two of them are deployed, it comes across as overkill. All three are tropes that put the character in situation hard to navigate because of mysterious forces.)
Now, despite their obvious commonalities, whether geography or architecture is in effect produces enormously different effects on the story.
Non-Euclidean geography is a property of the world. Everyone must deal with it. Nobody in Patricia C. Wrede's The Enchanted Forest Chronicles2, including the king, can fathom the nature of the forest, they can just cope with it.
It creates a world of strangeness and confusion, and perhaps wonders and marvels, or perhaps nightmares and horrors, if handled correctly.
It is true that a sufficiently powerful character could twist the world like that, at least for a region, but those characters tend to overwhelm your story if you let them on stage. Dead and legendary generally works best.
It can also work best for the architecture, but the building had to be built. Perhaps even by a character in the story.
At least, most of them. Some are so ancient, so powerful, even so bound into the very structure of the world, that it appears they were not built by any characters. James Stoddard's The High House has kingdoms within its rooms, a black river in its basement, and a dragon in its attic, and the forces that threaten it do so to threaten the world as a whole.
Even when the building was clearly made by characters, sometimes within the story, the range of non-Euclidean architecture goes from the dramatic edifice of legend, labyrinthine, significant, to a comic aspect of a cottage that is bigger on the inside than it is on the outside -- when that's made a point of. (A lot of buildings don't add up because the writer didn't think it through.)
But The Enchanted Forest Chronicles features a witch's cottage where one door leads from the kitchen to every other room in the cottage, though sometimes you have to be firm with it.
Harry Potter likewise uses it to compress the magical world into small spaces, and thus help the masquerade.
On the other hand, in Discworld, such locations as the home of Death, the library of the wizardly Unseen University, a temple to a Thing from the Dark Dimension, and places associated with the Fair Folk start with being bigger on the inside than on the outside. The University has a " Professor of Recondite Architecture and Origami Map Folding" whom other professors consult when trying to find a colleague's office.
It's important to be consistent. Even if it's to be consistent that "this trick to find your way works on Tuesdays, but on Wednesdays you might as well stay home, and on Thursdays, you must use this instead." Or a rhetorical consistency, so that it feels like the same place. If the weary travelers find the pine forest again, they know that they can find the Tangled Knot inn again, at least.
Any means by which the enemy can be tricked into an endless path, or the heroes can take a shortcut to forestall them, must be foreshadowed in the usual way.
I have done both geography and architecture, and have found both useful over the whole range.
In Winter's Curse3, the tower that was bigger on the inside than the outside was a useful clue about the power of a wizard whose power the two main characters had difficulty gauging.
In Spells In Secret4, one edifice they visited had corridors where doors and windows did not line up as they should have, befitting its nature. (The really labyrinthine edifice was Euclidean, as befit its nature.)
In Madeleine And The Mists5, the Misty Hills were entwined with such geography. Those who lived in them were not incorporated into the kingdom until after all the lands about them were, and even in the time of the book they were less so than other regions. Some paths crossed long distances in a day or two. Others last forever.
All of them had their uses in the work where I used them.
BTW, start with the fourth book and read the three prequels after
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It was a delight to see someone mention Stoddard's High House. it's one of my favorite and most inventive fantasy novels.
And talking non-Euclidean geography, I seem to recall that classic Dr. Seuss books and art had a lot of it.
In Christopher Nuttall's Schooled In Magic, there's Whitehall School Of Magic which is Larger On The Inside Than It is On The Outside.
While new Students at first have trouble finding their way around the school, generally the School doesn't attempt to fool them.
Of course, there are other places in that World (called the Nameless World) that are really "interesting", especially places where the Ancient Faerie made their home.