Bonding and coordination of oxygen in a Ga2O3 crystal structure I'm trying to find the crystal structure of gallium oxide ($\ce{Ga2O3}$). However, I find the images of the crystal structure in the peer-reviewed journals problematic.

First, I hop to the wikipedia article of Gallium oxide and find this image:

There was no labeling of the color, but I think Cyan is Gallium, and Red is Oxygen. The trouble is Ga typically has 3+ and Oxygen has 2- valence. Yet in this image we see Ga have 4 and 6 bonds! How is this possible?

The source is from a paper:  J. Åhman, G. Svensson and J. Albertsson: A Reinvestigation of β-Gallium Oxide. In: Acta Cryst. (1996). C52, 1336-1338. (The image was made by a wiki admin on chemistry structure, who made many structures for wikipedia.)

So I check out the article and it has this figure:

 

That's basically unreadable, so I go to Acta Crystallographica Section C and it has an interactive 3D chem model viewer and a model for Gallium Oxide:



Again I see Gallium with 6 bonds and oxygens with 3 bond! Is this correct? please tell me how?

In Galazka's β-Ga2O3 for wide-bandgap electronics and optoelectronics,I find this description:


  
  Crystal structure of $\ce{β-Ga2O3}$
  
  
  $\ce{β-Ga2O3}$ crystallizes in the base-centred monoclinic system in the
  space group C2/m. The unit cell (figure 1) contains 20 atoms
  consisting of crystallographically inequivalent $\ce{Ga^3+}$ and $\ce{O^2−}$ atoms. In this low symmetry structure Ga atoms are coordinated tetrahedrally and
  octahedrally (Ga1 and Ga2, respectively), while O atoms are
  coordinated three and fourfold (O1/O2 and O3, respectively). O1 shares
  two bonds with Ga2 and one bond with Ga1, O2 shares three bonds with
  Ga2 and one bond with Ga1, while O3 shares two bonds with Ga1 and one
  bond with Ga2. The lattice parameters of $\ce{β-Ga2O3}$ are listed in table
  1. There are two easy cleavage planes: the (100) plane formed by O3 atoms and (001) plane formed by O1 atoms.


and this figure:



Can someone please explain the crystal structure of $\ce{Ga2O3}$, beta-gallium oxide?
Does it help if you think of this as an ionic compound? In ionic compounds, there are no directed bonds. The coordination number depends on the size of the ions, coupled with the need for electroneutrality.

For example, in calcium oxide, both calcium and oxygen (in red) have octahedral coordination, with 6 neighbors each:

 

Granted, the electronegativity difference in calcium oxide is 2.44, while in gallium oxide it is only 1.65, and not different from that of silicon oxide, which has a network covalent structure.

Also, consider structure like that of hexagonal ice, where each oxygen is surrounded by four hydrogen atoms, two connected by covalent bonds, and two connected by hydrogen bonds. In this case, the atomic distances are clearly different, and you would be correct to say that oxygen makes two bonds, with a tetrahedral coordination if you consider the hydrogen atoms from neighboring atoms.

To distinguish these three extremes (ionic bonds in one case, covalent bonds plus contacts with neighboring atoms, network covalent structure) and to categorize what is going on with gallium oxide, you would have to look at the gallium oxygen bond lengths, which should be available in the paper you cite.