Symmetry, tiling, area, and fitting things together — usually at the same time, because a piece of the right shape still has to leave the rest of the board coverable.
Kajitsu asks for morsels that fold or spin onto themselves on a hexagonal grid, where intuition trained on squares is not much use. Hitome’s Garden cuts a surface into regions by deciding, line by line, which way a wall runs. Mondrian Puzzle tiles a canvas with rectangles no two of which may be the same shape. Fractured Fractions cuts one picture into four with a single point. Lozenge Land draws a heap of stone blocks as a flat tiling of rhombuses, and the whole puzzle is reading it as 3-D. No Three in a Line builds a city of towers on a field of dots with no three on one straight line, and keeps each biggest city beside its quarter turns and mirror images. Diversity City cuts a square into squares and scores each one by how many different sizes share an edge with it, so where a square goes matters as much as how big it is. Minotaur lays a string across a room of dots with every step longer than the last, and a slanted step is only measured by the right triangle under it. Galaxea, Zebra, Voronoi Islands and Ariadne’s String are two-player games about shape: where a rectangle may hang, which stones end up touching, where to stand so that the border halfway to the next iguana falls your way, and how far a thread can still step in a hall the other thread is crossing too.