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Common net of a 1x1x5 and 1x2x3 cuboid. Common nets of cuboids have been deeply researched, mainly by Uehara and coworkers. To the moment, common nets of up to three cuboids have been found, It has, however, been proven that there exist infinitely many examples of nets that can be folded into more than one polyhedra. [10]
The net has to be such that the straight line is fully within it, and one may have to consider several nets to see which gives the shortest path. For example, in the case of a cube , if the points are on adjacent faces one candidate for the shortest path is the path crossing the common edge; the shortest path of this kind is found using a net ...
Stella: Polyhedron Navigator Stella (software) - Can create and print nets for all of Wenninger's polyhedron models. Vladimir Bulatov's Polyhedra Stellations Applet; Vladimir Bulatov's Polyhedra Stellations Applet packaged as an OS X application Archived 2016-03-04 at the Wayback Machine
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A rectangular cuboid with integer edges, as well as integer face diagonals, is called an Euler brick; for example with sides 44, 117, and 240. A perfect cuboid is an Euler brick whose space diagonal is also an integer. It is currently unknown whether a perfect cuboid actually exists. [6] The number of different nets for a simple cube is 11 ...
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A cuboid is a convex polyhedron whose polyhedral graph is the same as that of a cube. [1] [2] General cuboids have many different types. When all of the rectangular cuboid's edges are equal in length, it results in a cube, with six square faces and adjacent faces meeting at right angles.