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Updated: September 27, 2025


The sight of a line of battle of twenty thousand Isosceles suddenly facing about, and exchanging the sombre black of their bases for the orange of the two sides including their acute angle; the militia of the Equilateral Triangles tricoloured in red, white, and blue; the mauve, ultra-marine, gamboge, and burnt umber of the Square artillerymen rapidly rotating near their vermillion guns; the dashing and flashing of the five-coloured and six-coloured Pentagons and Hexagons careering across the field in their offices of surgeons, geometricians and aides-de-camp all these may well have been sufficient to render credible the famous story how an illustrious Circle, overcome by the artistic beauty of the forces under his command, threw aside his marshal's baton and his royal crown, exclaiming that he henceforth exchanged them for the artist's pencil.

Q. Are there more than one sort of hexagons? A. Yes, there are regular and irregular. Q. What is a regular hexagon? A. When the sides and angles are all equal. Q. What is an irregular hexagon? A. When the sides and angles are not equal. Hept-agon. Q. What is this? A. A regular heptagon. Q. Why is it called a heptagon? A. Because it has seven sides and seven angles.

And when the shiftings of the Metal Hordes permitted we saw that all the flat floor of the valley was stripped and checkered, stippled and tessellated with every color, patterned with enormous lozenges and squares, rhomboids and parallelograms, pentagons and hexagons and diamonds, lunettes, circles and spirals; harlequined yet harmonious; instinct with a grotesque suggestion of a super-Futurism.

Through crooked, narrow streets, with houses overhanging and thrusting out corners and gables, houses with stables below, and quaint carvings and odd little windows above, the panes of glass hexagons, so that the windows looked like sections of honey-comb, we found our way to the inn, a many-storied chalet, with stairs on the outside, stone floors in the upper passages, and no end of queer rooms; built right in the midst of other houses as odd, decorated with German-text carving, from the windows of which the occupants could look in upon us, if they had cared to do so; but they did not.

The residences of some sixty of the most eminent professors of various sciences elected by their colleagues as seats fall vacant, with the approval of the highest Court of Judicature and of the camptâ cluster around a huge building in the form of a hexagon made up of a multitude of smaller hexagons, in the centre whereof is the great hall of the same shape.

There seemed to be every pattern that the ingenuity of woman could devise and the industry of woman put together, "four-patches," "nine-patches," "log-cabins," "wild-goose chases," "rising suns," hexagons, diamonds, and only Aunt Jane knows what else. As for color, a Sandwich Islander would have danced with joy at the sight of those reds, purples, yellows, and greens.

My carpets have been altered to fit all sized odd-shaped apartments from parallelopiped to hexagons. Much of my furniture has been distributed among my former dwellings. These limbs have stretched upon uncarpeted floors, or have been let down suddenly from imperfectly established bedsteads. I have dined in the parlor and slept in the back kitchen.

Yet these dexterous artists must view, with hopeless emulation, the hexagons and pyramids of the cells of a beehive: these fortitudinous heroes are awed by the superior fierceness of the lions and tigers; and in their amorous enjoyments they are much inferior to the vigor of the grossest and most sordid quadrupeds.

There is a theory, originally propounded by Buffon and now revived, which assumes that the bees have not the least intention of constructing hexagons with a pyramidal base, but that their desire is merely to contrive round cells in the wax; only, that as their neighbours, and those at work on the opposite side of the comb, are digging at the same moment and with the same intentions, the points where the cells meet must of necessity become hexagonal.

The archivault is ornamented on each side with sculptured wreaths of ivy, pine cones, branches of grapes and olives, interlaced with ribands. The ceiling of the portico is divided into hexagons and squares, enriched by various designs in the shape of eggs and roses, finely executed.

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