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A Möbius strip made with paper and adhesive tape. In mathematics, a Möbius strip, Möbius band, or Möbius loop[a] is a surface that can be formed by attaching the ends of a strip of paper together with a half-twist. As a mathematical object, it was discovered by Johann Benedict Listing and August Ferdinand Möbius in 1858, but it had already ...
A stellated icosahedron made from custom papers. 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 ...
The missing square puzzle is an optical illusion used in mathematics classes to help students reason about geometrical figures; or rather to teach them not to reason using figures, but to use only textual descriptions and the axioms of geometry. It depicts two arrangements made of similar shapes in slightly different configurations.
Arbitrary shapes, beyond symmetrical polyhedra, can also be constructed; a deltahedron with 2N faces and 3N edges requires 3N Sonobe modules. A popular class of arbitrary shapes consists of assemblies of equal size cubes in a regular cubic grid, which can be easily derived from the six unit cube by joining multiple ones at faces or edges.
Net (polyhedron) A net of a regular dodecahedron. The eleven nets of a cube. In geometry, a net of a polyhedron is an arrangement of non-overlapping edge -joined polygons in the plane which can be folded (along edges) to become the faces of the polyhedron. Polyhedral nets are a useful aid to the study of polyhedra and solid geometry in general ...
The cube can also be dissected into 48 smaller instances of this same characteristic 3-orthoscheme (just one way, by all of its symmetry planes at once). The characteristic tetrahedron of the cube is an example of a Heronian tetrahedron. Every regular polytope, including the regular tetrahedron, has its characteristic orthoscheme. There is a 3 ...
An Infinity cube made of dice being played with. An animation showing different moves and states of the Infinity cube (click to animate) An Infinity cube is a kind of mechanical puzzle toy with mathematical principles. Its shape is similar to a 2×2 Rubik's cube. It can be opened and put back together from different directions, thus creating a ...
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.
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