In geometry, the oblong is any rectangle that’s not also a square—or as non-geometrists call it, any “rectangle.” In word forms, it’s a rectangle balanced on one of its end points, like so (read across and down):
Windmills look like overlapping word squares:
Lattices are like windmills, but with more “crossbars” at the top, bottom, and sides, giving them a window-like appearance:
The “fan” consists of three linked triangles which have answer words going across always, in one diagonal downward direction, and not in the other except for the biggest, triangle-spanning word in that direction. Like so:
At the risk of editorializing, I think the diagonality of this form is less elegant than the forms you read horizontally and vertically. The two diagonal downward directions are equally valid, but to build a construction of much size, form constructors have to prioritize one such reading direction over the other. A puzzle structure can make the intended reading directions clear, but in the across-and-down forms, those directions are more intuitive.
The same issue is found in other diagonal constructions like the star, the pyramidal windmill, and…the Pygmy hourglass?
The star shown above has across and rightward-down answers. So does the unfortunately named hourglass at right—it’s named for a wordsmith whose last name was Pygmy, but even so, I think calling it a “word hourglass” is probably a better idea than taking time out to explain that. The pyramidal windmill, in the center, has across and down answers and one rightward-down that joins the structure together.
Next time out, we’ll get into one more simple form—and how it further challenges the definition of a crossword that the experts have tried to establish.
Thank you for sharing your great research in word "forms"