Paradzayi, I do not know if you want to create those hexagons for a real country or just have an exercise in computer simulation. In the 1st case you need to understand how it works economically, and I can give you some ideas.

The idea of Christaller about central places is the construction of regular hexagons. It was applied to Southern Germany; see https://blogs.ethz.ch/prespecific/2013/05/01/diagrams-christaller-central-place-theory/ . However, real pattern in regular only with some approximation. Large cities form nodes of the first order. Then one need to look for smaller places around, not always there are 6. See the attached picture for real application by Christaller.

One need to understand why this is relevant. The first basis is in spatial competition when transport cost is accounted for. Here you can start from the work of Hotelling (1929) about 2 sellers of ice-cream. In real 2-dimensional space hexagon is natural outcome. You can find a good review here: Handbook of Regional and Urban Economics. Vol. I. Regional Economics. Editor Peter Nijkamp. 1986. ch.2 by J.-F.Thisse & M.Beckmann.

Another reason for polycentric urban structures (not so common in literature) is in optimality of cities of different sizes, because there is a trade off between more types of services in a larger city and high living cost. You may have a look at my working paper with Trullen: https://www.researchgate.net/publication/275019830_Polycentric_Urban_Models

Research Polycentric Urban Models

 Yuri, many thanks for your timely response to my question. Your article improved my comprehension of the theory. Thanks. Let me clarify my question. With real geolocation data, I found that Voronoi tessellations are the closest I can get to Christaller's regular hexagonal polygons. With simulated regularly spaced geolocation data, Voronoi tessellations are regular squares (the Voronoi algorithm run in QGIS). Is there a way of specifying the number of vertices for the polygon in some other program that you or anyone knows about. I am good with R so code-based suggestions are welcome as well. 

Hexagons can be created with GRASS GIS (open source). See here for an example:

https://grass.osgeo.org/grass72/manuals/v.mkgrid.html#creating-hexagons-in-a-metric-projection

Thanks Markus. I am yet to try the procedure in Grass but I am sure it will work. Thanks a lot pal