All decks: every possible silhouette

From the enumeration we got 72,994 distinct (front, side) pairs. We can do a nice analysis on those. Namely, which decks can be formed, so that every pair (with all rotations and reflections) of front and side views are constructable.

First, we construct the distinct silhouettes (under $D_4$). It turns out that there are 102 distinct silhouettes, of which only 12 are printed in the Project Cube deck. So pick any subset S of those 102 shapes: when does S form a valid deck — every pair of cards in S, in any rotation, having a strict solution? And what are the largest such subsets?

We can construct a compatibility graph from this, listing all views and drawing an edge between them if there is at least one strict solution between them (for every rotation). As a note, I did not check if a card can be used with a copy of itself. All solutions are on GitHub and this analysis can be added there.

When not all pieces need to be used

When all pieces need to be used

The silhouette pair solver uses these graphs' edges as its lookup table — every pair you can draw on the front and side grids is one entry in the subset-allowed graph above.

The three largest cliques (subset-allowed regime)

There are 71 maximal cliques of size ≥ 2 in the subset-allowed graph. The three biggest all have 15 nodes; no clique grows past that.

(Each clique block below also lists a min STRICT number. That's the smallest STRICT count for any pair of cards in the clique, in any orientation. It's the "weakest link": the rarest strict solution you'd ever face if you played with this entire clique as your deck. A min STRICT of 1 means somewhere in the clique there's a card pair with exactly one matching tower.)

The all-pieces-required regime

Recompute the same exercise against the stricter graph (the one that requires every tower to use all six pieces, second figure above). The graph has 79 maximal cliques of size ≥ 2 instead of 71, but they're smaller — the largest is now 13 nodes, the next two are 12. Three game-card shapes that were comfortably part of every top-3 subset-allowed clique drop out of the top cliques here: cards 8 (), 10 (), 12 () and 14 () do not appear among the top three anymore.