Shapes of Hexagrams

J. Math. Sci. Univ. Tokyo
Vol. 6 (1999), No. 3, Page 539--558.

Ahara, Kazushi ; Yamada, Kinji
Shapes of Hexagrams
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We consider the set of similarity classes of hexagrams. If we fix a set of angles of hexagrams, the set of similarity classes can be identified with a hyperbolic hexahedron as in Figure 3, 4. We show that the space of angles (with some conditions) is a fiber bundle over the isometry classes of such hexahedra. The fibers are identified with a hyperbolic plane, and a dihedral group action on the set of angles is compatible with the hyperbolic structures on the fibers.

Keywords: hyperbolic geometry, similarity class, moduli space

Mathematics Subject Classification (1991): 57M50, 53C15
Mathematical Reviews Number: MR1726682

Received: 1999-01-11