Structure of Metallic Hydrogen
As annav states, the labeling H1, H2 etc is labeling of hydrogen atoms within a graphene-like hexagonal ring structure. Another way of looking at it, is in the image below:



Image source

In an article published after the web article you link to, Aromaticity, closed-shell effects, and metallization of hydrogen. (Abstract only), the authors confirm that


  Recent theoretical and experimental studies reveal that compressed molecular hydrogen at 200-350 GPa transforms to layered structures consisting of distorted graphene sheets.


This structure, according to the article, forms a stable structure at those pressures.  As per the comments, this is form graphene-like hydrogen, the abstract goes further, discussing the process that would result in hydrogen metallization:


  Metallization occurs upon further compression by destroying the closed shell electronic structure, which is mainly determined by the 1s electrons via lowering of the bonding bands stemming from the unoccupied atomic 2s and 2p orbitals.


This metallization of hydrogen is, according to the article High temperature superconductivity in sulfur and selenium hydrides at high pressure theorised to occur at pressures of 400 GPa or greater.