On objects that are frequently seen from different sides are found forms that are symmetrical both ways, when seen right and left and when seen up and down. Examples of this are the Australian shield fig. 22 (p. 33), and the parfleches of the North American Indians (fig. 89, p. 97). On objects of similar character made by the same technical processes and by the same tribe, such as rawhide bags (fig. 28) double symmetry may also occur. [Illustration: Fig. 28. Painted rawhide bags, Shuswap, British Columbia.] [Illustration: Fig. 30. Carved board Kaiserin Augusta Fluss, New Guinea.] In circular forms the diameter is often the axis of symmetry. In other cases symmetrical fields are radially arranged and there may be a number of repetitions. The circumference takes the place of the horizontal, the radius that of the vertical (fig. 29). [Illustration: Fig. 29. Designs of the Dayak.] In a number of cases we find instead of normal symmetry an inversion of the two symmetrical halves so that what is above to the right, is below to the left. Arrangements of this type are, however, less numerous than true symmetry. Such forms occur in New Guinea. They are due to the decorative development of the two branches of a double spiral (fig. 30). This form results sometimes from circular rhythmic repetitions in which the whole circle is filled by two or more units. This is found for instance, in pottery from the southwestern Pueblos (fig. 31) and also quite commonly in Central America.[26] [26] See, for instance S. K. Lothrop, Pottery of Costa Rica and Nicaragua, New York, 1926, Plates 39, 46, fig. 195. [Illustration: Fig. 31. Designs from pottery of the ancient Pueblos.] Other figures resulting from rotation, that is from a decorative pattern applied rhythmically in the same direction, as for instance the swastika and S shaped figures occupying the center of a decorative field, present the same type of inverted symmetry. The same treatment is found in the art of ancient Scandinavia (fig. 32). [Illustration: Fig. 32. Bronze ornament, Sweden, 7th Century A. D.] [Illustration: Fig. 33. Design from Peruvian textile.] A curious development of this decorative device is applied in the art of ancient Peru. On many fabrics we find patterns consisting of a diagonal arrangement of squares or rectangles. In each diagonal the same design is repeated, while the next diagonal has another type. In each diagonal line the design is shown in varying positions. If the one faces the right, the next faces the left. At the same time there is an alternation of colors, so that even when the form is the same, the tints and the color values will not be the same. A characteristic specimen of this type will be described later on (p. 47).