Answer: PINE
Summit Wei

This is a meta about geometric solids (polyhedra). This is clued punnily by "solid" in the title. Each feeder answer can be associated with a geometric solid.

Feeder answer Solid Explanation
ASSOCIATION FOOTBALL Truncated icosahedron Soccer balls are tiled as truncated icosahedra.
TLACHIHUALTEPETL Square-base pyramid Tlachihualtepetl is a square-base pyramid. (Technically, it's slightly different because of the layer sizes, but it's close enough to being one.)
ROLLS FOR INITIATIVE Icosahedron In DND, one rolls for initiative with an icosahedral die.
THE DARK SIDE OF THE MOON Triangular prism On the album cover, there's an image of a triangular prism refracting light.
DOUBLE PLANETOID Stellated octahedron The M.C. Escher print is in the shape of a stellated octahedron.
BY ANY OTHER NAME Cuboctahedron In the Star Trek episode, some of the Enterprise crew members are transformed into cuboctahedrons.
HURRY-SCURRY GALAXY Rhombicuboctahedron The planet in the galaxy is in the shape of a rhombicuboctahedron.

In addition, "different lengths" in the flavor clues that each of the answers for this meta have different lengths from 13 to 20, which provides a sorting mechanism. Afterwards, we use the Vertex, Edge, and Face count of each solid and plug them into the expressions in order.

Shape V E F Result
Cuboctahedron 12 24 14 8482
Stellated octahedron 8 12 8 6969
Square pyramid 5 8 5 8773
Rhombicuboctahedron 24 48 26 8472
Icosahedron 12 30 20 6779
Truncated icosahedron 60 90 32 7869
Triangular prism 6 9 5 8352

Finally, hinted at by "askiing", we take every two digits and translate them into a number in ASCII. Reading the letters in order, The result is TREEWITHCONES4, a crossword clue with answer PINE.

Author's Notes

This meta was constructed around the answer THE DARK SIDE OF THE MOON, because I really wanted to write a feeder using moon names as a dataset. Meta writer privileges :p