Heptomino

When rotations and reflections are not considered to be distinct shapes, there are 108 different free heptominoes.

Thus, only 4 heptominoes fail to satisfy the criterion and, in fact, these 4 are unable to tessellate the plane.

[5] It is also impossible to pack them into a 757-square rectangle with a one-square hole because 757 is a prime number.

However, the set of 107 simply connected free heptominoes—that is, the ones without the hole—can tile a 7 by 107 (749-square) rectangle.

[6] Furthermore, the complete set of free heptominoes can tile three 11-by-23 (253-square) rectangles, each with a one-square hole in the center; the complete set can also tile twelve 8 by 8 (64-square) squares with a one-square hole in the "center".