The Dungeon Geomorphs were originally 3 separate products published in 1976 and 1977. (My digital version of the collected set -- as shown above -- doesn't actually credit Gygax anywhere, but his name was on the cover of the earlier sets that you can see at the Acaeum site over here.)
Thus, there are 3 different "sets" of geomorphs, identified as "Basic Dungeon", "Caves & Caverns", and "Lower Dungeons". Each has 15 different sections of dungeon architecture (lettered A-O) that can be combined and connected in different ways to create unique dungeon layouts. Each page of the product has 3 sections: 2 sections 21x21 squares each, and 1 section sized 10x42 squares (each square 10', per the introduction). All together, my estimate is that there's upwards of 1,000 separate rooms and passages pictured in the Geomorphs, so it provides a good look at Gygax's design sensibilities at the time.
First, a quick sense of each of the different set types:
- Basic Dungeon. The first thing that strikes me here is that almost the entirety of each map page is covered with accessible rooms -- there is almost no "dark space" of solid rock to speak of. (Module B1, 1st level is the only other dungeon product that looks similar to me.) While it's easy to get lost here, the overall sense is one of "openness", of being able to access every part of the map with some effort. There are lots of rooms here (estimate: 35 rooms and 20 passages per map section).
- Caves and Caverns. As to be expected, these levels have irregular, rough-hewn tunnels and cave systems. There's a lot more dark space, as adjacent areas are almost always separated by at least 10' of rock (instead of thin one-line walls like in the Basic Dungeon). Caves tend to be larger than the rooms elsewhere, and unlike the other sets, there are no doors anywhere. Due to the larger sized caves, there are far fewer of them per page (estimate: 6 caves and 20 tunnels per section).
- Lower Dungeons. The lower dungeons have more of a "claustrophobic" feel to them. There's more dark space than in the Basic Dungeon (a balance between thin-line and 10' block room dividers), and I think the rooms are, on average, smaller. There are more odd-shaped rooms, zig-zag passages, several isolated 30' circles (possibly chutes/shafts bypassing the level?), a number of 10x10' room maze areas with many doors, etc. There are more rooms than in the caves levels, but fewer than the Basic Dungeon (estimate: 20 rooms and 20 passages per section).
Now, considerations of features shared across the different set types:
Doors: Excepting the Caves levels, there are doors (and secret doors) indicated throughout the different sections, although some rooms are missing doors, and thus disconnected from the rest. (The Introduction makes clear that you're expected add doors, delete or modify areas, etc.) There are a small number of these disconnected rooms in the Basic Dungeon, and a larger number of them in the Lower Dungeons areas (some sections more than others).
Passages: The vast majority of passages, corridors, and tunnels are 10' wide, rarely 20', and never any larger than that. About half of the Basic Dungeon tiles (8 of 15) have a single straight piece of 20' wide corridor, stretching about two-thirds the way across the tile. Arguably, there are no 20' corridors in any of the Caves or Lower sets; there are some 20' wide areas which might be interpreted as either cave/rooms or corridors, but in any case they're much shorter than in the Basic Dungeon. Even in the Caves levels, there are many 10' wide tunnels that run straight along a cardinal direction (to me, reminiscent of the sample tunnel sections in the module D1-3 product).
Central Areas: A common feature shared across all the sets is that each provides 3 sections that can be joined to create an enormous central area location -- perhaps a grand Arena/Cavern/Temple area. (Respectively these are sections ILF, ILO, and ILO in each of the 3 sets.) If joined, each of the versions of the huge central feature is about 22 squares on each side or somewhat larger (i.e., over 200 feet square).
Diagonals: One issue that motivated this overall article was the burning question: "How many diagonal features did Gygax expect to use on a typical dungeon map?". While design elements in the four cardinal directions (NSEW) are easy to deal with on graph paper, those on a non-cardinal 45 degree axis (NE, NW, SE, SW) tend to aggravate me, my players, my geometry sensibilities, and my software projects (see here). So I'll pay particularly close attention to those elements, to see how widespread they were expected to be.
Here's an overview of the diagonal situation: (1) While diagonal passages appear on almost every dungeon section, they are limited in scope -- usually only 30' of corridor or so. (2) Diagonal passages are always 10' wide, never a 20' wide passage or anything bigger. And importantly: (3) Practically every square/rectangular room in the product (the vast majority of rooms) is oriented in the cardinal direction, regardless of whether the approaching corridors are on a diagonal or not. (There are only two exceptional occurrences of square rooms oriented on the diagonal -- one in Basic Dungeon Section N, upper left corner; and a pair of connected rooms in Lower Dungeons Section C, upper left corner.)
Finally, a listing of recurring unusual room shape elements (having noted that the vast majority of rooms are square or rectangular in shape):
- Circles. In the Basic Dungeon, there are some 20' wide circular areas, each one a dead-end with no door (4 of these). There are a few 30' wide round areas (3 of these), in each case the nexus of 4 diagonal corridors. As noted earlier, the Lower Dungeons have some 30' wide circular rooms (3) that are almost totally disconnected from their surroundings. There are also 3 zones of sweeping, curved corridor around these areas.
- Triangles. Where a diagonal corridor is placed, this tends to create a triangular room on each side, at least in the Basic Dungeon sections (or else possibly a trapezoid; see below). Practically all of these are right-angle isosceles triangles (i.e., a right angle and two equal sides; or, a 45-45-90 degree triangle). Generally, the two equal legs are on the cardinal axes, with the hypotenuse on the diagonal -- in the Basic Dungeon, this is true 46/53 = 87% of the time, while in the Lower Dungeons it's only true 14/27 = 52% of the time. In the Lower Dungeons, it's common to construct triangular rooms by chopping a 20x20' square room in half (5 instances) or to cut one large "cardinal" triangle into two smaller "off-cardinal" triangles (3 instances).
- Trapezoids. Where a diagonal corridor doesn't create a triangular room to the side, it might create a right-angle trapezoid -- almost a rectangle, but with one diagonal wall (at least in the Basic Dungeon). In almost every case of this, 3 walls are connected by right angles and lay in the cardinal directions; the 4th connecting wall is on the 45-degree diagonal.
- Octagons. There are several locations in the Basic Dungeon (5) with 30'-wide octagons, always used in a similar fashion to the 30' circles -- as the junction for a 4-way corridor intersection. In these cases, the corridors are always running in the cardinal directions (not diagonal).
- Stepwise. This would be a room that was perhaps trying to be triangular or trapezoidal, but was made "pixellated", with one or two of the walls running zig-zag along the boundaries between grid squares. This happens several times (6) in the Lower Dungeons.
Typical usage of each of these element types can be seen below: