4.3. WHAT ABOUT REFLECTIONS?225also asked to find a formula for the reflection through a plane that does notpass through the origin.A reflection that sends a geometric figure onto itself is a type of sym-metry of the figure. It is not an actual motion that you could perform on aphysical model of the figure, but it is an ideal motion.Let’s see how we can bring reflection symmetry into our account ofthe symmetries of some simple geometric figures. Consider a thickenedversion of our rectangular card: a rectangular brick. Place the brick withits faces parallel to the coordinate planes and with its centroid at the originof coordinates. See Figure4.3.2.r2r1r3Figure 4.3.2.Rotations and reflections of a brick.The rotational symmetries of the brick are the same as those of therectangular card. There are four rotational symmetries: the nonmotion
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