Later examination showed it to be a colossal joke. The book did catalog over 600 patterns, many by Loyd himself. In this context, it means that there are no indentations along the outside edge. There are only 13 silhouettes that qualify. Other finite sets may exist.
Tangrams continue to entertain and frustrate now days.
The puzzle attracts people on a number of levels. It gets the math inclined with the geometry and ratios of the pieces. The figures spark visually inclined people though their form, liveliness and striking simplicity. It is one of the classic puzzles, appealing to young and old, the serious and the carefree. Go make one and enjoy it.