Steven Dutch, Professor Emeritus, Natural and Applied Sciences, University of Wisconsin  Green Bay
At left is a polyhedral model of the olivine structure. The oxygens are in a nearly closepacked arrangement.
Si tetrahedra cap voids in the zigzag chains of Mg octahedra. 

Here is a ball model of the structure. Blue atoms are oxygen, magenta are silicon, and yellow are magnesium. 
The diagram below shows two layers of the structure, showing how successive layers are related.
The figure below shows how the magnesium atoms (yellow and green) relate to the silica tetrahedra (shown with blue oxygen atoms and magenta silicon).
All of these structures look quite nearly hexagonal, and in fact the b/c ratio of the unit cell is 1.71, not far from the square root of 3 (1.732). Thus the diagonal of the unit cell nearly forms a 3060 right triangle with the two adjacent edges.
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Created 21 February 2002, Last Update 31 May 2020