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Etymologically, "cuboid" means "like a cube", in the sense of a convex solid which can be transformed into a cube (by adjusting the lengths of its edges and the angles between its adjacent faces). 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.
Cube – , where is the side's length; Cuboid – a b c {\textstyle abc} , where a {\textstyle a} , b {\textstyle b} , and c {\textstyle c} are the sides' length; Cylinder – π r 2 h {\textstyle \pi r^{2}h} , where r {\textstyle r} is the base's radius and h {\textstyle h} is the cone's height;
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.
In the case of the body cuboid, the body (space) diagonal g is irrational. 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]
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 ...
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]
In physics, there are equations in every field to relate physical quantities to each other and perform calculations. Entire handbooks of equations can only summarize most of the full subject, else are highly specialized within a certain field.
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.