All-Natural Gem Polish

What's really magical here is that all the gems are flawless.

"In a mine, where a million diamonds shine!"
—Snow White and The Seven Dwarfs

In real life, gem appraising, cutting, polishing, faceting, etc. is a multibillion dollar industry. Not so in fiction. Not only are they much bigger, they're just naturally flawlessly cut and perfectly shiny, even while they're still in the ground, or where there's no logical way they could have been cut. Characters will find these gems studding the walls of a mine, lying close to the surface, or lying casually in open fields. Bonus points if there's also large clumps of different types, as seen in the page picture. Any place where they're abundant is usually a City of Gold.

While tumbled pebble gems may look "polished," and really good mineral samples can have well-formed crystals, most of the ones commonly considered very valuable (diamonds, emeralds, sapphires and rubies) do require quite a bit of work to be presentable. In the rough, they look like all other dirty, randomly shaped rocks. The common gem shapes seen in jewelry stores aren't naturally present in any gem. The circular diamond with a pointed bottom, rectangular emerald, and perfectly rounded opal were designed that way to best showcase the gem (for instance, the "brilliant" cut for diamonds maximizes their sparkle by angling reflected light back through the top of the stone).

This is probably an Omnipresent Trope. Subtrope to Artistic License Geology. Related to the Rule of Perception (as many viewers would be unable to identify uncut gems as such without being explicitly told what they are) and could lead to Reality Is Unrealistic. Not related to All-Natural Snake Oil.

Examples of All-Natural Gem Polish include:

Comic Books

Superman in the Silver Age and Bronze Age was known for squeezing lumps of coal into diamonds. Aside from being bad science for other reasons, the diamond produced was always a cut diamond with facets.

Film

This occurs in Happily N'Ever After.^[context?]
Jurassic Park has someone pull amber out of a mine, and it is shiny already. All the miners did was grind off some of the rock in which the amber was encased.
In Snow White and The Seven Dwarfs, the dwarfs' mine has a huge variety of gems that are all already perfectly cut. Doc's evaluations aren't even really about their carats, but whether they "sound" good via tapping them.
In Congo, the diamonds in the ancient mine are already sufficiently well cut that one can be plugged straight into a commercial laser for huge power boost.
- Bonus points in that the heroine gets (easily) a blackstone that a dead guy had been holding for some years in his hand, smashes it, get the perfectly cut diamond, and somehow it manages to fit exactly in the laser that they have been carrying for the whole movie.^[1]

Literature

This occurs in Lloyd Alexander's Chronicles of Prydain novel The High King. While going through a Fair Folk mine tunnel, Glew finds a large number of uncut gems that are sparkling, glinting and glittering. (Homage is paid to the trope though: Doli comments that those stones are really worthless, and even the work of a jeweler wouldn't improve them much.)
Averted in The Phantom Tollbooth the Numbers Mine is of the ordinary sort. Carts of rough stone are being pushed around, and men are explicitly sitting at buffing wheels on site. The Mathemagician has to reach into their carts to get polished stones. The weird thing is; the residents of Digitopolis consider diamonds, emeralds, etc. to be worthless, yet they still polish and cut them before tossing them out.

Live-Action TV

In an episode of Saturday Night Live hosted by Christopher Reeve, there was a sketch showing how Reeve got the Superman part. He screws up the "turning coal into diamonds" bit by using too much pressure, but gets the part anyway.
In an episode of The Adventures of Superman, Superman made a new diamond to replace a diamond in a native statue in the jungles of the Amazon.
In Smallville, Clark squeezes a lump of coal into a cut diamond and uses his heat vision to set it in a ring for Lana. Of course, that whole episode ended up not happening.

Video Games

With the addition of mining for ores, The Elder Scrolls V: Skyrim allows the player to also occasionally find precious gems. Most of the time this trope is averted, with the gems being rough and flawed, but occasionally, the Dovakhiin can dig up a perfectly flawless, pre-cut gemstone. Out of an iron vein.
The more primitive mining system from The Elder Scrolls III: Morrowind featured diamond veins that looked like elongated, beautiful bluish-white crystals poking out of a boulder. You can take cut diamonds from it.
In Mega Man 9, Jewel Man's stage has enormous pre-cut gems inside the ground.
Jazz Jackrabbit has enormous pre-cut gems inside the ground, too.
In Minecraft, while some materials, such as iron and gold, have to mined as unrefined blocks and then smelted into usable forms, diamonds pop out of the wall as the aforementioned symmetrical, visibly faceted lumps.
Any jewel or precious stone mined in the Harvest Moon and Rune Factory series. Curiously, precious metals do not come already in bar form.
During Kingdom of Loathing's 2011 Crimbo (read: Christmas) event, players could mine at the Gummi Mines, carving out rock candy that was "already in convenient ingot form".
- Its three other existing mines also sometimes have stones of eXtreme power or lumps of (cut) diamond in them, but considering they include ores like cardboard, linoleum or velcro, expecting gems to be cut is the natural thing to do.
In Spelunky, gems mined from rocks are as much polished as ones found in treasure chests or on ground.

Web Comics

Erfworld justifies this since it takes place in a Tabletop Games world and explicitly doesn't follow real life physics.

Western Animation

In My Little Pony: Friendship Is Magic, all of the gems Rarity finds are cut in various shapes. As are the ones Spike eats. Even the turquoise he eats in Appleloosa, while not cut into faceted shapes, appears as polished nuggets, which is not typical of turquoise found in real life.
On The Simpsons, the mine run by a crazy woman using enslaved apes in Africa has gems like this.

Aversions

Literature

Phule's Company had a Lampshaded aversion. Phule's dialogue with the local gemstone magnate goes like this:

Charlie: In fact, I've got 'em with me if you'd like to see. (shows a handful of pebbles)
Phule: Uh... Very nice.
Charlie: (shows his ring) ...This is what they end up lookin' like.
Phule: (really meaning it this time) Very nice.

In The Phantom Tollbooth the Numbers Mine is of the ordinary sort. Carts of rough stone are being pushed around, and men are explicitly sitting at buffing wheels on site. The Mathemagician has to reach into their carts to get polished stones. The weird thing is; the residents of Digitopolis consider diamonds, emeralds, etc. to be worthless, yet they still polish and cut them before tossing them out.
In the second Artemis Fowl, Mulch Diggums uses dwarfish rock polish to melt a window to break into a home; he pauses in his internal monologue to mock humans as he does so, for cutting gems to make them presentable, which he considers to be a waste of gemstone.
A good portion of Airman takes place at a prison where the prisoners mine diamonds. At one point, a guard frustrated at being unable to stop a supposed boogeyman starts chucking uncut diamonds into the sea, thinking they're just rocks. A smarter guard notices them for what they are, and realizes the "boogeyman" is actually part of a heist.
In Twenty One Balloons, the diamond mine of Krakatoa is explicitly stated to have the diamonds as lumpy rocks. The founder of the island has to shatter one of them into planes to form an axe blade.
In King Solomons Mines the cache of diamonds is composed of uncut and rough-cut stones, the largest of which are badly flawed and/or off-colour.

Video Games

RuneScape - mined gems are uncut. In order to use them in jewelery, the Crafting skill is required to cut them first. It also gets into the realistic zone in that the gems don't just lie on the ground but have to be mined - and in that certain gems are found with certain ores.
The dwarves in Dwarf Fortress mine out rough gems that need to be cut before they're usable. The later versions even have different kinds of cuts, depending on the type of gem.
The Sims 3 includes rough gems (and unrefined ore) scattered around the town that sims can pick up and send away to be cut into numerous different designs. Some gems have special properties that can't be used until after they've been cut.
In Harvest Moon: Animal Parade, you find uncut "Wonderfuls" of various colors in the mine. They're next to worthless unless you have Mira cut and refine them, and she has a good chance of failing, too, meaning you'll want to mine a lot if you want to find all the good gems.
Diablo II's socketed items can be fitted with gems of many grades, the lowest being Chipped and the highest being Perfect. The game also has the refining process present in the Horadric Cube.
World of Warcraft has an entire Jewelcrafting profession available, in which the player takes raw gemstones and grinds and polishes them into something usable in Socketed Equipment. Jewelcrafting also gives the prospecting skill that allows a player to sacrifice raw metal ore for a chance to find raw gems.
Averted in Secret of Shadow Ranch, in which getting an agate polished is actually necessary to obtain a clue.
In the flash game Ravenwood Fair, gems fresh from the mine are uncut and lumpy. A machine to cut and polish them must be obtained by completing challenges.
In Arcanum, not only all the gems are either found in chests or obviously dropped on the floor by somebody, but there are rough jewels, which look like misshapen shards of coloured glass and, of course, cost less.

↑ First oF all; there were TONS of polished diamonds in the ground, that could have been cut by the previous (and killed) party, but she had to use that one. Second: if you want to get something that a long-dead body has been grasped for months, you'll have to break its fingers. Third: She broke the rock, but it could be a diamond or just coal. Fourth: Diamonds are fragile, if you do that, it's more easy to break the diamond inside than the coal outside. Fifth, the very issue of being polished. And finally, it matches EXACTLY the size of the laser gun. Why in this world would you make a gun that needs an Applied Phlebotinum that you don't know exists is beyond anyone's wit.

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[1] First oF all; there were TONS of polished diamonds in the ground, that could have been cut by the previous (and killed) party, but she had to use that one. Second: if you want to get something that a long-dead body has been grasped for months, you'll have to break its fingers. Third: She broke the rock, but it could be a diamond or just coal. Fourth: Diamonds are fragile, if you do that, it's more easy to break the diamond inside than the coal outside. Fifth, the very issue of being polished. And finally, it matches EXACTLY the size of the laser gun. Why in this world would you make a gun that needs an Applied Phlebotinum that you don't know exists is beyond anyone's wit.