When computer solvers became easy to code and run, when computer power allowed a lot of calculation in little time, it became possible to look for shapes with the heighest number of solutions.
| Property | Value for trihexes | Value for pentiamonds | Notes |
|---|---|---|---|
| Type of cells | hexagons | triangles | |
| Number of cells per piece | 3 | 5 | |
| Number of pieces | 3 | 4 | |
| Symmetrical pieces | 3 | 2 | |
| Number of possible connected shapes | 951 | 491 030 | A measure of a sets scope of shapes. A very heigh proportion are without esthetic or functional value, though. |
| Symmetrical connected shapes | 6 | 66 | Esthetically satisfying shapes -- polyform enthusiasts rarely construct assymetric shapes. |
| Connected shapes with holes | 10 | 90,702 | Because of the geometry of the triangular grid, most of the holes share a summit with the edge of the shape itself. This is impossible with polyhexes but possible with squares. |
| Largest farm (fully enclosed hole) | 2 | 8 | The hole touches the edge of the shape via a single summit in the case of the pentiamonds. |
| Number of largest farms | 1 | 1 | |
| Most distinct holes in a shape | 1 | 3 | |
| Shapes with most holes | 10 | 8 | |
| Maximal number of solutions per shape | 4 | 4 | A measure of a set's combinatorial complexity. |
| Number of shapes with most solutions (Champion shapes) | 2 | 5 | |
| Minimal perimeter of a connected shape | 22 | 12 | These are the most compact shapes that can be formed with the set. |
| Number of shapes with minimal perimeter | 1 | 7 | |
| Number of convex connected shapes | 0 | 1 | There are no convex shapes for polyhexes and only rectangles work with polyominoes. So this property is meaningful only for polyiamonds. There is just one convex pentiamond shape, for instance, as it has been proved by George Sicherman. |