Origami Polyhedra Design by John Montroll PDF

By John Montroll

This e-book unravels the secret of Geometry in Origami with a special process: sixty four Polyhedra designs, each one made up of a unmarried sq. sheet of paper, no cuts, no glue; every one polyhedron the most important attainable from the beginning dimension of sq. and every having an inventive locking mechanism to carry its form.

the writer covers the 5 Platonic solids (cube, tetrahedron, octahedron, icosahedron and dodecahedron). There are considerable diversifications with diversified colour styles and sunken aspects. Dipyramids and Dimpled Dipyramids, unexplored earlier than this in Origami, also are lined. There are a complete of sixty four types within the ebook. all of the designs have an attractive glance and a lovely folding series and are in response to special mathematical equations

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Odd symmetry. 3/4 square symmetry. Crease Patterns After experimenting with these crease patterns, this one was chosen. It yields the largest model that has the fewest steps and holds together well. If it does not maximize the size of the model, then it is very close to it and appears to maximize with respect to its simplicity. It uses 3/4 square symmetry. 42 Part I: Designing Origami Polyhedra 3/4 square symmetry. Landmarks Given the crease pattern, the landmarks are to be found. 1. Find α. Triangular face.

Find c. 5 d c Design Method Examples 43 4. Find e. 1464466 = (2 − 2) 4 α α f e 5. Find g, first find k. 2679491 = tan(15°). 2679491 = tan(15°) Of these, a and g are easy to find and sufficient for completing the folding pattern. 5°). 2679491 = tan(15°). 44 Part I: Designing Origami Polyhedra 1 2 15° Fold and unfold. 2679491 = tan(15°) Polygons Since polygons are the faces of polyhedra, we present how to fold certain polygons before we move into folding directions for polyhedra. Many of the polyhedra in this collection have faces that are regular polygons, which are polygons with congruent angles and sides.

1 2 Fold and unfold along the diagonal. Fold and unfold to the diagonal. 41421356 24 Part I: Designing Origami Polyhedra Dividing a Square into nths First, some specific cases will be shown. Then some general methods will be given. Divisions of 1/3 1 2 3 4 5 1/3 Fold and unfold in half on the left. Unfold. Crease at the bottom. Fold and unfold on the right. The 1/3 mark. 198912. 5%). 1 2 3 4 5 1/5 Fold and unfold creasing along part of the diagonal. Crease on the left. Unfold. Fold to the crease and unfold.

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