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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]
A cuboid has twelve face diagonals (two on each of the six faces), and it has four space diagonals. [2] The cuboid's face diagonals can have up to three different lengths, since the faces come in congruent pairs and the two diagonals on any face are equal. The cuboid's space diagonals all have the same length.
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 ...
A magic square is an arrangement of numbers in a square grid so that the sum of the numbers along every row, column, and diagonal is the same. Similarly, one may define a magic cube to be an arrangement of numbers in a cubical grid so that the sum of the numbers on the four space diagonals must be the same as the sum of the numbers in each row, each column, and each pillar.
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.
A cuboid, a topological cube, has 8 vertices, 12 edges, and 6 quadrilateral faces, making it a type of hexahedron. In the context of meshes, a cuboid is often called a hexahedron, hex, or brick. [1] For the same cell amount, the accuracy of solutions in hexahedral meshes is the highest.
Four-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space (3D). Three-dimensional space is the simplest possible abstraction of the observation that one needs only three numbers, called dimensions, to describe the sizes or locations of objects in the everyday world.
C 4v, [4], (*422): if one face has a different color (or two opposite faces have colors different from each other and from the other four), the cube has 8 isometries, like a square has in 2D. D 2h, [2,2], (*222): if opposite faces have the same colors, different for each set of two, the cube has 8 isometries, like a cuboid.