A geomantic figure is exhausted by its four rows of one or two points. Everything else the tradition says about it was added afterwards.
The pattern
Tristitia is double, double, double, single, reading Fire, Air, Water and Earth from the top down, seven points in all. Three heavy rows sit above one light one, giving a broad body over a narrow base. It is the mirror image of Laetitia, and the two names, sorrow and joy, sit opposite each other in the Latin as the shapes do on the page.
Flipping every row
Change each row from single to double and from double to single and Tristitia becomes Cauda Draconis, not Laetitia. This is the point at which the structure stops matching the intuition: the figure that looks like the opposite of Tristitia is not the one the flip produces, because turning a figure upside down and inverting each of its rows are different operations that give different results.
Two operations, often confused
Reversing the order of the four rows and inverting the state of each row are separate transformations. Some authors use both, under Latin names that are not applied consistently from book to book. The atlas therefore describes the operation performed rather than naming it, so that a reader can carry the description into any handbook.
The attributions
The planet, sign and element recorded for this figure come from the astrological layer, differ between the Latin sources, and are recorded here as tradition rather than as fact about the points.