The former question may be investigated in two ways: By studying the variety of forms which are used to represent the same objects, and conversely by illustrating the variety of explanations given to the same form. Arapaho designs collected by Kroeber offer a favourable field for this study. The range of forms interpreted as the star (fig. 96) is based on the tendency in the art of the Plains Indians to use triangular and quadrangular figures and narrow lines, and on the scarcity of polygons. We find, therefore, as representations of stars, crosses, groups of squares, diamonds and a cross with triangular wings. In the last quite exceptional figure of this series the star is represented by a hexagon. In some cases the association between the form and its meaning becomes more intelligible through the general setting in which the design element is found, as for instance, through the color contrast between design and background.[55] [55] See A. L. Kroeber “The Arapaho”, Bulletin of the American Museum of Natural History, Vol. 17. The variety of forms which are used to represent a person may serve as another example (fig. 97). Some of these are similar to the forms used to represent the star. Still another example is the representation of the butterfly (fig. 98). In this series one of the designs representing the star will be found. [Illustration: Fig. 97. Patterns representing persons, Arapaho.] [Illustration: Fig. 98. Patterns representing butterfly, Arapaho.] [Illustration: Fig. 99. Examples of chevrons from Neu-Mecklenburg; _a_, Carved bamboo; _b_, Embroidered mat. The chevron to the left on the bamboo represents a palm leaf, an armring or a worm; the same design on the mat, tracks of a crustacean.] Conversely a diamond is explained as a person, a turtle, the navel, a mountain, a lake, a star, an eye. The setting of the design does not by any means explain sufficiently why these varying interpretations should be used. A rectangle represents a camp circle, brush hut, a mountain, the earth, a buffalo or life; a triangle with an enclosed rectangular or pentagonal figure (see fig. 117, p. 120) is explained as a mountain with trees, a cave in the mountain, a brush hut or a tent. The second form in fig. 98 is explained as a butterfly or the morning-star. In bead embroidery we find frequently a central design in the form of a diamond, from the acute angles of which, extend straight lines. To the ends of these triangular designs or other small forms are attached. In fig. 152 (p. 178) some of these designs are shown. The first one is taken from a pouch (_j_); the central diamond represents a person, the triangular designs at the ends of the lines, buffalo hoofs. A similar design (_k_) from a moccasin represents the navel and arrows; the background is snow. In a third example (_q_) the central diamond represents a turtle, the lines its claws and the small patterns at the ends of these lines, eggs.