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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.
Cuboid: a, b = the sides of the cuboid's base c = the third side of the cuboid Right-rectangular pyramid: a, b = the sides of the base h = the distance is from base ...
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 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.
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 cube is a special case of rectangular cuboid in which the edges are equal in length. [1] Like other cuboids, every face of a cube has four vertices, each of which connects with three congruent lines. These edges form square faces, making the dihedral angle of a cube between every two adjacent squares being the interior angle of a square, 90 ...
The hexagonal packing of circles on a 2-dimensional Euclidean plane. These problems are mathematically distinct from the ideas in the circle packing theorem.The related circle packing problem deals with packing circles, possibly of different sizes, on a surface, for instance the plane or a sphere.
The parallelepiped with D 4h symmetry is known as a square cuboid, which has two square faces and four congruent rectangular faces. The parallelepiped with D 3d symmetry is known as a trigonal trapezohedron , which has six congruent rhombic faces (also called an isohedral rhombohedron ).