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  2. Rectangular cuboid - Wikipedia

    en.wikipedia.org/wiki/Rectangular_cuboid

    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 ...

  3. Cuboid - Wikipedia

    en.wikipedia.org/wiki/Cuboid

    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. [1] [3] Along with the rectangular cuboids ...

  4. Euler brick - Wikipedia

    en.wikipedia.org/wiki/Euler_brick

    For the edge cuboid, one of the edges a, b, c is irrational. The face cuboid has one of the face diagonals d, e, f irrational. The body cuboid is commonly referred to as the Euler cuboid in honor of Leonhard Euler, who discussed this type of cuboid. [15] He was also aware of face cuboids, and provided the (104, 153, 672) example. [16]

  5. Hoffman's packing puzzle - Wikipedia

    en.wikipedia.org/wiki/Hoffman's_packing_puzzle

    The puzzle itself consists only of 27 identical rectangular cuboid-shaped blocks, although physical realizations of the puzzle also typically supply a cubical box to fit the blocks into. If the three lengths of the block edges are x , y , and z , then the cube should have edge length x + y + z .

  6. The spider and the fly problem - Wikipedia

    en.wikipedia.org/wiki/The_spider_and_the_fly_problem

    Depending on the dimensions of the cuboid, and on the initial positions of the spider and fly, one or another of these paths, or of four other paths, may be the optimal solution. [4] However, there is no rectangular cuboid, and two points on the cuboid, for which the shortest path passes through all six faces of the cuboid. [5]

  7. Solid geometry - Wikipedia

    en.wikipedia.org/wiki/Solid_geometry

    A cube, except that its faces are not squares but rhombi; Cuboid: A convex polyhedron bounded by six quadrilateral faces, whose polyhedral graph is the same as that of a cube [4] Some sources also require that each of the faces is a rectangle (so each pair of adjacent faces meets in a right angle).

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