EXAMPLE 1 Bakuba Patterns

We use the flowchart of Figure 19.13 to analyze some of the Bakuba patterns of Figure 19.11.

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Figure 19.11a does not have a vertical reflection, so we branch right, and the pattern notation begins to take shape as . The figure has neither a horizontal reflection nor a glide reflection, so we branch right again, filling in the third position in the notation to get . A half-turn preserves part of but not all the pattern, so we conclude that we have a pattern.

Figure 19.11b does not have vertical reflection, so we branch right to . The figure does have horizontal reflection, so we branch left and left, concluding that the pattern is .

Figure 19.11f has vertical reflection, so we branch left to . The figure does not have horizontal reflection, so we branch right but cannot yet fill in the third symbol. The figure does have a half-turn symmetry (and glide symmetry), with its center on the middle of the three lines between any pair of closest triangles. So the pattern is .