The Crystal Palace pane of glass (49 inches) as the hypotenuse of a right-angled triangle, thereby creating a triangle with a length-to-height ratio of 2.5:1, whose base (adjacent side) was 4 feet long. By mirroring this triangle he obtained the 8-foot-wide gables that formed the vertical faces at either end of the prism, each of which was 24' long. With this arrangement, Paxton could glaze the entire roof surface with identical panes that did not need to be trimmed. Paxton placed three of these 8' x 24' roof units side-by-side, horizontally supported by a grid of cast iron beams, which was held up
Automedian triangle satisfying the formula "a" = "b" + "c". That is, in order for the three numbers "a", "b", and "c" to be the sides of an automedian triangle, the sequence of three squared side lengths "b", "a", and "c" should form an arithmetic progression. If "x", "y", and "z" are the three sides of a right triangle, sorted in increasing order by size, and if 2"x" < "z", then "z", "x" + "y", and "y" − "x" are the three sides of an automedian triangle. For instance, the right triangle with side lengths 5, 12, and 13 can be used