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In another there is a square, together with five rectangles in which the length is always equal to the side of the square while the breadth gradually decreases. In another drawer there are six regular polygons containing from five to ten sides, i.e., the pentagon, hexagon, heptagon, octagon, nonagon, and decagon.
It is even conceivable that an insect might, by fixing on a point at which to commence a cell, and then moving outside, first to one point, and then to five other points, at the proper relative distances from the central point and from each other, strike the planes of intersection, and so make an isolated hexagon: but I am not aware that any such case has been observed; nor would any good be derived from a single hexagon being built, as in its construction more materials would be required than for a cylinder.
Stopping at the largest public building in the city, a central hexagon with a number of smaller hexagons rising around it, we entered one of the latter, each side of which might be some 30 feet in length and 15 in height.
Nothing would induce an aspiring Isosceles, who has hopes of generating an Equilateral Son, to take a wife who reckoned a single Irregularity among her Ancestors; a Square or Pentagon, who is confident that his family is steadily on the rise, does not inquire above the five-hundredth generation; a Hexagon or Dodecagon is even more careless of the wife's pedigree; but a Circle has been known deliberately to take a wife who has had an Irregular Great-Grandfather, and all because of some slight superiority of lustre, or because of the charms of a low voice which, with us, even more than with you, is thought "an excellent thing in a Woman."
Every side of your hexagon, of which you will determine the length in proportion to the dimensions taken upon the place, will be divided into two parts and upon the middle point you will elevate a perpendicular towards the center of the polygon, which will equal in length the sixth part of the side.
In the centre of the floor-space six little cut logs were fastened down in the form of a hexagon, and the earth scooped from within the hexagon was banked against the logs to form a permanent and limited fireplace.
These were less regular, certainly, than those of an ordinary comb; wherefore the queen, having inspected them, wisely declined to lay any eggs there, for the generation that would have arisen therefrom would necessarily have been deformed. Each cell, however, was a perfect hexagon; nor did it contain a single crooked line, a single curved figure or angle.
The first point, therefore, is to expand this space as far as possible, and that in a form more convenient than the circle for the adjustment of the stones above. In general the square is a more convenient form than any other; but the hexagon or octagon is sometimes better fitted for masses of work which divide in six or eight directions. XX. This is the abacus.
"Instead of making use of the square or rectangle, as has been done to this time, you will suppose your place inclosed in a regular hexagon, this polygon having the advantage of offering more angles than the quadrilateral one.
R. Cooke, who had, the inscriptions tell us, become a prebendary in 1660. Each cup has engraved on it a copy of the common seal of the dean and chapter, with Dr. Cooke's arms above. The button bases of the patens bear the donor's crest. The insides of the bowls, except the nearly vertical rims, are embossed with a honeycomb pattern, and beneath each hexagon here, there is a plain circle outside.
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