Download A Constellation of Origami Polyhedra by John Montroll PDF

By John Montroll

N this interesting consultant for paperfolders, origami specialist John Montroll presents uncomplicated instructions and obviously distinct diagrams for growing striking polyhedra. step by step directions exhibit easy methods to create 34 diverse types. Grouped in line with point of trouble, the versions variety from the straightforward Triangular Diamond and the Pyramid, to the extra advanced Icosahedron and the hugely not easy Dimpled Snub dice and the exceptional Stella Octangula.

A problem to devotees of the traditional eastern paintings of paperfolding, those multifaceted marvels also will entice scholars and an individual drawn to geometrical configurations.

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The remainder were contained in a stack of papers a foot high! ) Pattern A B C D E F G H I J 6 x 10 5 x 12 4 x 15 Figure 40. Total Number of Solutions 7 (one shown) 1 0 1 11 1 1 1 4 1 15 12 2 Table 3. 30 Geometric Puzzle Design At the beginning of the Cornucopia project, as the computer started to spew out solutions, we wondered if any subset would be found that made all 13 patterns. Preliminary results indicated this to be very unlikely. To our surprise, however, near the end of the run, one prolific subset, the Copious Cornucopia, was discovered that failed to do so by the narrowest margin.

Perhaps it is because the two solutions are quickly memorized, and then there are no more problems. But there are exceptions. The Sam Loyd dissection puzzle described in the previous section was most likely developed by dissecting the square into the cross, after which the other interesting problem shapes were probably discovered. Creative Puzzles of the World by van Delft and Botermans contains an excellent chapter on geometric dissections as practical puzzles. Further investigation might uncover a dissection by which several polygons could be constructed from a neat set of pieces.

Designs with only one solution are consid- 16 Geometric Puzzle Design ered especially clever, but how do you know? ) 3. Pieces with compact shapes approximating square or rectangular, such as those containing a 2 × 2 square, lend themselves more easily to solutions and increase the number of solutions. Contrarily, skinny, angular, complicated shapes do just the opposite, especially those that refuse to fit into corners. 4. To be avoided are pieces having rotational symmetry and especially pieces identical to each other.

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