Unexpected data from the Large Hadron Collider suggest a new type of matter (opens in new tab)

You've got a good point, and there's lots of exotic types and in-betweens on Wikipedia which I didn't list. My list was to point out that we've named more than the 3 classical states of matter.

Why not? Because the energy of which it's composed doesn't interact with photons?

"Phases" are poorly defined. They exist wherever there's a statistical mechanics reason to define them, and they make sense only within the limits of the approximations on which they are based. Glass is "solid" to a mechanical engineer (in most regimes), but it's not a crystal and doesn't behave like one to a solid state physicist. Likewise "plasma" is a great tool to describe a fluorescent light bulb or lightning bolt, but not so much a white dwarf. Even stuff you think you understand, like "liquid and gas are clearly different" turns out to be wrong (http://en.wikipedia.org/wiki/Supercritical_fluid).

My impression was also incorrect. Wiki says it's an "amorphous solid" aka one that doesn't form into crystals.

https://en.wikipedia.org/wiki/Glass

There's also Amorphous Ice, which is arranged in a "glass-like" form: https://en.wikipedia.org/wiki/Amorphous_ice