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A chiliagram is a 1,000-sided star polygon. There are 199 regular forms [a] given by Schläfli symbols of the form {1000/n}, where n is an integer between 2 and 500 that is coprime to 1,000. There are also 300 regular star figures in the remaining cases. For example, the regular {1000/499} star polygon is constructed by 1000 nearly radial edges.
There are two traditional methods for making polyhedra out of paper: polyhedral nets and modular origami.In the net method, the faces of the polyhedron are placed to form an irregular shape on a flat sheet of paper, with some of these faces connected to each other within this shape; it is cut out and folded into the shape of the polyhedron, and the remaining pairs of faces are attached together.
A pentagon is a five-sided polygon. A regular pentagon has 5 equal edges and 5 equal angles. In geometry, a polygon is traditionally a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed chain.
In geometry, a uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other). It follows that all vertices are congruent, and the polyhedron has a high degree of reflectional and rotational symmetry.
Modular origami or unit origami is a multi-stage paper folding technique in which several, or sometimes many, sheets of paper are first folded into individual modules or units and then assembled into an integrated flat shape or three-dimensional structure, usually by inserting flaps into pockets created by the folding process. [3]
The following list of polygons, polyhedra and polytopes gives the names of various classes of polytopes and lists some specific examples. Polytope elements ...
Net templates are then made. One way is to copy templates from a polyhedron-making book, such as Magnus Wenninger's Polyhedron Models, 1974 (ISBN 0-521-09859-9). A second way is drawing faces on paper or with computer-aided design software and then drawing on them the polyhedron's edges. The exposed nets of the faces are then traced or printed ...
Geometric Folding Algorithms: Linkages, Origami, Polyhedra is a monograph on the mathematics and computational geometry of mechanical linkages, paper folding, and polyhedral nets, by Erik Demaine and Joseph O'Rourke. It was published in 2007 by Cambridge University Press (ISBN 978-0-521-85757-4).