By John Montroll
N this attention-grabbing consultant for paperfolders, origami specialist John Montroll offers easy instructions and obviously certain diagrams for growing impressive polyhedra. step by step directions exhibit find out how to create 34 assorted versions. Grouped in response to point of trouble, the types diversity from the straightforward Triangular Diamond and the Pyramid, to the extra advanced Icosahedron and the hugely tough Dimpled Snub dice and the superb Stella Octangula.
A problem to devotees of the traditional eastern paintings of paperfolding, those multifaceted marvels also will entice scholars and a person drawn to geometrical configurations.
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Extra info for A Constellation of Origami Polyhedra
9. T. Adachi and S. Maeda, Holomorphic helix of proper order 3 on a complex hyperbolic plane, Topology and its Applications (Elsevier Science) 146/147 (2005), 201–207. 10. T. Adachi and S. Maeda, Curves and submanifolds in rank one symmetric spaces, Amer. Math. , A Translation of Sugaku Expositions 19 (2006), 217–235. 11. T. Adachi and S. Maeda, Integral curves of the characteristic vector field of real hypersurfaces in nonflat complex space forms, Geometriae Dedicata 123 (2006), 65–72. 12. T. Adachi and S.
Here M can be identified with M/ I . In this way, if f : M → R3 is a conformal minimal surface and there is an antiholomorphic involution I : M → M without fixed points so that f ◦ I = f , then we can define a non-orientable minimal surface f : M = M/ I → R3 . Conversely, every non-orientable minimal surface is obtained in this procedure. Suppose that f : M = M/ I → R3 is complete and of finite total curvature. 1 to the conformal minimal immersion f : M → R3 . Furthermore, we have a stronger restriction on the topology of M or M .
S. Maeda and H. Tanabe, Totally geodesic immersions of K¨ ahler manifolds and K¨ ahler Frenet curves, Math. Z. 252 (2006), 787–795. 39. S. Maeda and K. Tsukada, Isotropic immersions into a real space form, Canad. Math. Bull. 37 (1994), 245–253. 40. S. Maeda and S. Udagawa, Characterization of parallel isometric immersions of space forms into space forms in the class of isotropic immersions, Canadian J. Math. 61 (2009), 641-655. Received August 7, 2012. jp Dedicated to Professor Sadahiro Maeda on his 60th birthday We have shown  that if the projective developing map of a regular curve in the sphere is injective then the curve has no self-intersection.
A Constellation of Origami Polyhedra by John Montroll