Permit me one brief sanity diversion with an excerpt from the book, The Honey Bee, by James L. Gould and Carol Grant Gould. Though it is written from an evolutionary perspective, the authors frequently cannot help but use the language of design in attempting to describe the phenonenon. Here's one example;
"...Beeswax is a fatlike substance that is metabolically expensive to produce: a kilogram of honey plus an undetermined amount of pollen is converted into only 60 grams of wax; it takes about 7 kilograms of honey to produce the comb in an average hive.
The cells are built according to a design that minimizes the use of this expensive commodity; a kilogram of wax is sufficient to work into 80,000 cells. Less social bees generally build cells on a horizontal surface; bumble bees, for instance, most often use the floor of an abandoned underground mouse nest. The cells are basically cylindrical pots arranged in a hodge-podge manner, sometimes sharing a thick wall, sometimes not. In a honey bee colony, the cells are arranged in an efficient hexagonal grid, with every cell sharing a wall with six adjacent cells. The comb hangs down vertically from the top of the cavity, and every cell shares its base with cells opening on the other side of the two-layer structure. The cells are not quite horizontal, but rather tip up 13° from their bases; this helps keep the nectar and honey from oozing out. Moreover, the cells on the two sides are offset slightly, so that the center of a base on one side is the junction of three walls on the other, an arrangement that adds greatly to the strength of the comb. The result of this architectural scheme is that the wax can be incredibly thin: the walls are only eight-hundredths of a millimeter thick, and the base (which forms the backbone of the comb) is only two-tenths. Feather light and brittle, the comb can nevertheless support many kilograms of honey. In especially hot climates, where the comb tends to soften and lose its essential rigidity, the bees mix propolis with the wax flakes during construction to create a strong alloy." (p. 31) [emphasis mine]
Cordially,
Certainly the honeycomb is a fascinating structure. But I still don't see where you are adequately supporting the design conclusion. If a resource is as biologically expensive to produce as beeswax and honey, does it not follow that the most successful colonies would be the ones to make most efficient use of said resource?
I don't see believe you are suggesting that the bees themselves designed the honeycomb. They are merely reproducing a pattern within an available space. Unless you are saying that the bees are designed, and therefore the comb is designed. Unfortunately, that method of classification requires that one must first identify the creator of an object in order to arrive at the design conclusion.
I think PatrickHenry summed it up when he asked (paraphrased), "Can naturally occuring artifacts give the appearance designed?" On the flip side, can an intelligent agent create an artifact that is not designed? And just to throw a third monkeywrench into the works, what would you say of the following two paintings? Are either of them designed? Would it surprise you to learn that the creator of one of them is not human? Can you tell which one?

Abstract oil painting

Abstract watercolor painting
On a personal note, best wishes to you and your family. Get some sleep.