Abstract
THE following simple construction shows in one figure all the elements of a cell of a honey-comb. On two rectangular axes take OA and OB equal to the side and diagonal of a square Join AB and bisect it in c. Draw CD normal to AB. Join AD, and complete the rhombus whose sides are AD, DB. Then if OA be a side of the hexagon, A D B E is one of the three equal planes forming the trihedral angle which closes the cell. The three short diagonals D E meet in the vertex of the cell, and are normal to each other. The three long diagonals A B form an equilateral triangle. O D is the height of the vertex above the hexagonal face of the prism. A E D is the angle which the axis of the prism makes with each of the diagonals D E. A D O is the angle which the axis of the prism makes with each of the edges of the trihedral angle. The diagonals D E and A B are in the ratio of the side and diagonal of a square. Such a cell contains a maximum volume with a minimum surface.
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GEOGHEGAN, E. The Cell of the Bee. Nature 18, 385 (1878). https://doi.org/10.1038/018385a0
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DOI: https://doi.org/10.1038/018385a0
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