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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.
DNA origami object from viral DNA visualized by electron tomography. [1] The map is at the top and atomic model of the DNA colored below. (Deposited in EMDB EMD-2210) . DNA origami is the nanoscale folding of DNA to create arbitrary two- and three-dimensional shapes at the nanoscale.
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 ...
"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
The March 1, 1943, edition of Life magazine included a photographic essay titled "Life Presents R. Buckminster Fuller's Dymaxion World", illustrating a projection onto a cuboctahedron, including several examples of possible arrangements of the square and triangular pieces, and a pull-out section of one-sided magazine pages with the map faces printed on them, intended to be cut out and glued to ...
The Miura fold is a form of rigid origami, meaning that the fold can be carried out by a continuous motion in which, at each step, each parallelogram is completely flat. This property allows it to be used to fold surfaces made of rigid materials, making it distinct from the Kresling fold and Yoshimura fold which cannot be rigidly folded and ...
The fold-and-cut problem asks what shapes can be obtained by folding a piece of paper flat, and making a single straight complete cut. The solution, known as the fold-and-cut theorem, states that any shape with straight sides can be obtained. A practical problem is how to fold a map so that it may be manipulated with minimal effort or movements.
It consists of building a mirror-symmetrical crease pattern and then collapsing it to find a finished form, usually a geometric shape such as a cube. He also discovered and proved that with any given flat point in an origami model, the sum of alternating angles is always equal to 180 degrees, a result now known as Kawasaki's theorem .
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