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If a net is given together with a pattern for gluing its edges together, such that each vertex of the resulting shape has positive angular defect and such that the sum of these defects is exactly 4 π, then there necessarily exists exactly one polyhedron that can be folded from it; this is Alexandrov's uniqueness theorem. However, the ...
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.
Net In geometry , the Rhombicosidodecahedron is an Archimedean solid , one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces . It has a total of 62 faces: 20 regular triangular faces, 30 square faces, 12 regular pentagonal faces, with 60 vertices , and 120 edges .
"3D convex uniform polyhedra o3o5x – doe". Editable printable net of a dodecahedron with interactive 3D view; The Uniform Polyhedra; Origami Polyhedra – Models made with Modular Origami; Virtual Reality Polyhedra The Encyclopedia of Polyhedra; K.J.M. MacLean, A Geometric Analysis of the Five Platonic Solids and Other Semi-Regular Polyhedra
Solid Body Viewer is an interactive 3D polyhedron viewer which allows you to save the model in svg, stl or obj format. Interactive Folding/Unfolding Platonic Solids Archived 2007-02-09 at the Wayback Machine in Java; Paper models of the Platonic solids created using nets generated by Stella software; Platonic Solids Free paper models (nets)
3D model of a truncated icosahedron In geometry , the truncated icosahedron is a polyhedron that can be constructed by truncating all of the regular icosahedron 's vertices. Intuitively, it may be regarded as footballs (or soccer balls) that are typically patterned with white hexagons and black pentagons.
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).
The Dalí cross, a net of a tesseract The tesseract can be unfolded into eight cubes into 3D space, just as the cube can be unfolded into six squares into 2D space.. In geometry, a tesseract or 4-cube is a four-dimensional hypercube, analogous to a two-dimensional square and a three-dimensional cube. [1]