|
A hexomino (or 6-omino) is a polyomino of order 6, that is, a polygon in the plane made of 6 equal-sized squares connected edge-to-edge. The name of this type of figure is formed with the prefix hex(a)-. When rotations and reflections are not considered to be distinct shapes, there are 35 different ''free'' hexominoes. When reflections are considered distinct, there are 60 ''one-sided'' hexominoes. When rotations are also considered distinct, there are 216 ''fixed'' hexominoes. ==Symmetry== The figure shows all possible free hexominoes, coloured according to their symmetry groups: * 20 hexominoes (coloured grey) have no symmetry. Their symmetry group consists only of the identity mapping. * 6 hexominoes (coloured red) have an axis of mirror symmetry parallel to the gridlines. Their symmetry group has two elements, the identity and a reflection in a line parallel to the sides of the squares. * 2 hexominoes (coloured green) have an axis of mirror symmetry at 45° to the gridlines. Their symmetry group has two elements, the identity and a diagonal reflection. * 5 hexominoes (coloured blue) have point symmetry, also known as rotational symmetry of order 2. Their symmetry group has two elements, the identity and the 180° rotation. * 2 hexominoes (coloured purple) have two axes of mirror symmetry, both parallel to the gridlines (thus one horizontal axis and one vertical axis). Their symmetry group has four elements. It is the dihedral group of order 2, also known as the Klein four-group. If reflections of a hexomino are considered distinct, as they are with one-sided hexominoes, then the first and fourth categories above would each double in size, resulting in an extra 25 hexominoes for a total of 60. If rotations are also considered distinct, then the hexominoes from the first category count eightfold, the ones from the next three categories count fourfold, and the ones from the last category count twice. This results in 20 × 8 + (6+2+5) × 4 + 2 × 2 = 216 fixed hexominoes. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Hexomino」の詳細全文を読む スポンサード リンク
|