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As far as I could find, we don't really have anything like the Star Trek alphabetized #planetary classification, at least not for rocky #planets. But we do have something for gas giants in the form of the Sudarsky classification based on spectra and temperature.
https://iopscience.iop.org/article/10.1086/309160

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"Jupiter Core" by XKCD comic (mirror bots @xkcd @xkcdbot ) - He starts with actual theories and then, as usual, gets distracted and his attention wanders off... Some shiny stuff.πŸͺ™πŸ΄β€β˜ οΈ So far no squirrels.πŸΏοΈπŸ• https://xkcd.com/3083/ #astronomy #planetary #space#WTF#humor
XKCD comic #3083 "Jupiter Core"

Transcript & explanation by ExplainXKCD https://www.explainxkcd.com/wiki/index.php/3083:_Jupiter_Core

Transcript:
Current leading theories for what's in the center of Jupiter:

[Variations of Jupiter, except for the last are shown with about 1/8 of the planet chopped off to show the core.]

[Jupiter with liquid material at its core]
Diffuse mix of heavy elements and metallic hydrogen

[Jupiter with a rocky core]
Rocky core with metallic, hydrogen mantle

[Jupiter with a pile of coins for a core, with multiple dollar signs shown]
Valuable treasure

[Jupiter with Earth for a core]
Emergency backup Earth

[Hollow Jupiter with a rocky planet in the middle]
Regular planet pretending to be a gas giant to avoid attention

[Jupiter with a smooth ball for a core]
Hard ball from avocado

[Jupiter with a small version of Jupiter for a core]
Baby Jupiter, still gestating

[Jupiter as a flat circle, with nothing chopped off]
No core; flat Earth conspiracists are wrong about Earth but right about Jupiter

title text: Juno mission data suggests that Jupiter actually contains Matryoshka doll-style nested copies of every other planet in the Solar System.

explanation (truncated to fit alt text):
Jupiter is the largest planet in the Solar System, the fifth planet from the Sun, and the closest-in gas giant. The core of the planet is hidden by an enormous gaseous atmosphere, and this comic lists a number of theories about the structure of that core. [...]
XKCD comic #3083 "Jupiter Core" Transcript & explanation by ExplainXKCD https://www.explainxkcd.com/wiki/index.php/3083:_Jupiter_Core Transcript: Current leading theories for what's in the center of Jupiter: [Variations of Jupiter, except for the last are shown with about 1/8 of the planet chopped off to show the core.] [Jupiter with liquid material at its core] Diffuse mix of heavy elements and metallic hydrogen [Jupiter with a rocky core] Rocky core with metallic, hydrogen mantle [Jupiter with a pile of coins for a core, with multiple dollar signs shown] Valuable treasure [Jupiter with Earth for a core] Emergency backup Earth [Hollow Jupiter with a rocky planet in the middle] Regular planet pretending to be a gas giant to avoid attention [Jupiter with a smooth ball for a core] Hard ball from avocado [Jupiter with a small version of Jupiter for a core] Baby Jupiter, still gestating [Jupiter as a flat circle, with nothing chopped off] No core; flat Earth conspiracists are wrong about Earth but right about Jupiter title text: Juno mission data suggests that Jupiter actually contains Matryoshka doll-style nested copies of every other planet in the Solar System. explanation (truncated to fit alt text): Jupiter is the largest planet in the Solar System, the fifth planet from the Sun, and the closest-in gas giant. The core of the planet is hidden by an enormous gaseous atmosphere, and this comic lists a number of theories about the structure of that core. [...]