19 Symmetry and Pattern

Self Check Answers

144
100
Translations, vertical reflections, half-turns, and glide reflections
$p m 11$
$p m a 2$
${I, V, H, R^{2}, R^{3}, D_{1}, D_{2}}$ , where $H$ and $V$ are horizontal and vertical reflection (as in the rectangle case), $R$ is a quarter turn, and $D_{1}$ and $D_{1}$ are reflections across the diagonals.
Both $VT$ and $T^{- 1} V$ produce $W_{e} W_{d} W_{c} W_{b} W_{a} \dots$ with $W_{b}$ in position 3 (the position of the axis of the vertical reflection $V$ ).

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