by Andy Boroson
Problem:

The “dead trees” in question are paper, and the five diagrams are origami crease patterns.

In origami terminology, convex folds are “mountain folds” and concave folds are “valley folds.” Here, solid lines indicate mountains and dashed lines indicate valleys.

Some solvers may be accustomed to dash-dot-dash-dot for mountain folds, as is standard in step-by-step origami instructions, but that convention isn’t generally followed in complete crease patterns. The flavor confirms the interpretation of “solid” as mountain, and “scattered” as valley, for those who are unsure.

Each design is based on box-pleating a 16×16 grid, which means they can readily be folded using unmarked paper of any size. Most solvers will probably just print and fold the actual diagrams.

When successfully folded, each diagram becomes a letter (or a design prominently featuring a letter) with some number of protruding tabs. On four of the letters these tabs are formed identically, as 2×1 rectangles; on the last one they're 1×1 variants of the same structure.

The letters take shape in several different ways, so that completing one isn’t likely to help the solver predict the structures of the others. They are presented in alphabetical order.

In the following diagrams:
Gray areas disappear into the interior and aren’t visible in the finished model. Red areas become tabs. Green areas become letters.

An A with 5 tabs, formed flat. The white areas correspond to the back of the finished letter. The vertex of the A doesn’t actually join; the two sides just overlap. (Any device for locking them together would have been ambiguous in the crease pattern.) Note that the crossbar collapses the entire middle of the paper, concertina-style. The angles where the sides meet the crossbar are notated on the diagram so as to deter folders from the temptation to straighten them out to a neat 45 degrees, which would result in an H rather than an A.

A G with 3 tabs, flat against a background. The letter is formed as though from a folded ribbon, using the left side of the paper collapsed concertina-style. The tabs are on the right, in a separate area, with an “arrow” pointing back at the G. (The two gray areas shown on the finished letter are spots where the underside of the paper is visible; they correspond to the reverse sides of the small shaded triangles on the crease pattern.)

An I with 4 tabs, formed as a 3D block letter. The green area here indicates just the front face. The rear is identical, except with a seam down the center.

An L with 1 tab, formed as a block letter extruded from a flat background. Quite a lot of paper gets collected into the lower-left-hand corner! The thick stack of layers there should lie flat against the “ceiling” on the underside of the L.

A U with 2 tabs, formed as a 3D block letter. The green area here indicates just the front face. The curve of the U is formed at both the top and bottom of the paper, and then the two curves lock tightly against each other, each forming half of the depth of the letter.

Ordering by the number of tabs spells the answer: LUGIA.