D8
The eight-sided die is an octohedron: one of the symmetrical polyhedra known as the "Platonic solids."

It looks like two pyramids having lezbo ass-to-ass sex.
A d8 was always used for hit points for Dungeons & Dragons monsters, and in Advanced D&D it was used for those classes that more hit points but weren't supposed to be as butch as Fighters or Paladins.
Eight-sided dice also have the most variations with weird not-numbers stuff on them, like compass directions, random weather, letters. They're also used as below-bargain-basement minifigs because one point is always off the table, like a big nose, or turret.
When you played Dragon Dice, the d8s were the terrain, which could change under your feet without moving your army, somehow.
James Ernest came up with a game "Dogfight" that uses d8s for their numbers, for being pointy and for turning in circles when you try to roll them like wheels... then he remembered that people put weird shit on d8s and he came up with a new game called "DiceLand." He even tried adapting Steve Jackson's OGRE to his d8 faggot-tree, but it didn't become popular enough to generate any grognard rage.