Homemade honeycomb tool racks

[morsa]

With “honeycomb” I mean a structure of adjoining (cylindrical, not hexagonal) cells.

Those who know of geometry could explain why (I suppose it is related to the concept of hexagon circumscribed in a circumference), but just by observation, it is a fact that whatever the diameter of a cylinder, the circumference can be filled with SIX cylinders of the same diameter, which is the basis of these racks.

They are made with reused items:

1) Arts and crafts tool rack. Made with tablet bottles and a container









2) Putty and gluing tool rack. Made with Crazy-glue containers and a deodorant bottle







3) Wooden dowels. Made with caulking tubes and a coffee can







Regards.

[morsa]

I was curious how many cylinders have to be used to make a second row around these six. Using a drawing of a honeycomb, I found some interesting facts:

1- Assuming all cylinders have the same diameter, a second row (orange) will have 12 units
2- The third row (yellow) would have 18 units
3- The fourth row (green) would have 24 units
4- The fifth (blue), 30 units and so on, that is, SIX more units for each new row
5- Even using cylinders, whatever the number of rows, the set will have a HEXAGONAL shape