By Energy Efficiency and Renewable Energy Clearinghouse (U.S.)
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2. 3. Rotation 1. 2. 4. Glide Reﬂection 1. 4. Glide Reﬂection Deﬁnition: a motif is translated and reﬂected, not necessarily in a straight line. This is the most complex form of symmetry and the one which can take the most time to understand fully. The deﬁnition given above is the strictest and most correct deﬁnition, but it is often relaxed to include any combination of translation and reﬂection symmetries. Rules are made to be broken and glide reﬂection symmetry is a prime example of how designs can be evolved by learning and then disregarding what has been learnt.
1. 2. Rotational : 058 BASIC PLEATS 2. 1. 2. 2 _ 1 This basic rotational Accordion pleat divides a 360° circle into 16 equal angles, recreating the Rotational Sixteenths examples on pages 24–25. 2 _ 2 Two semicircles are divided into sixteenths and joined end to end to create a letter ‘S’. The pattern could continue inﬁnitely. 2 _ 2 : 059 2. 1. 2. 3. 2 _ 3 Although the folds are rotational, no curved edges are used here. Note how all the folds would meet at an imaginary point. This example can be made quickly, without measuring any angles, using the Linear Sixteenths method (see pages 16–17).
Stretching and skewing can be combined very effectively with other basic concepts in this chapter, to create forms that are two or three times removed from an original crease pattern motif on a square of paper. These new folded forms can be highly sophisticated and unusual or – frankly – they can be rather contrived and tawdry. Only working with the paper in your hands will separate the good results from the not so good. 1. Stretch A square, when stretched in one speciﬁc direction, will create a rectangle.