TAOCP 7.2.2.1 Exercise 386
Solution to TAOCP 7.2.2.1 Exercise 386.
Section 7.2.2.1: Dancing Links
Exercise 386. ▶ [M31] A polyomino can have eight different types of symmetry:
| (i) | (ii) | (iii) | (iv) | (v) | (vi) | (vii) | (viii) |
|---|---|---|---|---|---|---|---|
| $\square$ | (shape) | (shape) | (shape) | (shape) | (shape) | (shape) | (shape) |
| full | 90° | 180° | biaxial | bidiagonal | axial | diagonal | none |
(Case (i) is often called 8-fold symmetry; case (iii) is often called central symmetry; case (vi) is often called left-right symmetry. Cases (ii), (iv), (v) are 4-fold symmetries; cases (ii) and (iii) are rotation symmetries; cases (iv)–(vii) are reflection symmetries.) In each case an $n$-omino of that symmetry type has been shown, where $n$ is minimum.
How many symmetry types can a polyiamond or polyhex have? Give example $n$-iamonds and $n$-hexes of each type, where $n$ is minimum.
Verified: no
Solve time: 3m21s