krychle

In Czech, krychle denotes what in English is called a cube. A cube is a regular hexahedral solid in three-dimensional geometry. It has six congruent square faces, twelve edges of equal length, and eight vertices. The faces meet at right angles, so the dihedral angle between any two adjacent faces is 90 degrees.

If the edge length is a, the cube’s volume is a^3 and its surface area is 6a^2. The space (body) diagonal, joining opposite vertices, has length a√3, while the diagonal of a single face is a√2.

A cube can be described conveniently by placing it with its center at the origin and its vertices at (±a/2, ±a/2, ±a/2). It is one of the five Platonic solids: all faces are congruent squares and all edges are equal.

In terms of symmetry, the cube has the octahedral symmetry group, with 24 rotational symmetries and 48 including reflections.

Common examples of cubes in everyday life include dice and the Rubik’s Cube, which is a mechanism-based puzzle built around a subdivided cube. The cube appears in many areas of mathematics, computer graphics, architecture, and design due to its simplicity and symmetry.