Cube

In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.

The cube is the only regular hexahedron and is one of the five Platonic solids and has 12 edges, 6 faces and 8 vertices.

The cube is also a square parallelepiped, an equilateral cuboid and a right rhombohedron. It is a regular square prism in three orientations, and a trigonal trapezohedron in four orientations.

The cube is dual to the octahedron. It has cubical or octahedral symmetry.

Orthogonal projections

The cube has four special orthogonal projections, centered, on a vertex, edges, face and normal to its vertex figure. The first and third correspond to the A₂ and B₂Coxeter planes.

Spherical tiling

The cube can also be represented as a spherical tiling, and projected onto the plane via a stereographic projection. This projection is conformal, preserving angles but not areas or lengths. Straight lines on the sphere are projected as circular arcs on the plane.

Vice

Vice is a practice, behavior, or habit generally considered immoral, sinful, criminal, rude, depraved, or degrading in the associated society. In more minor usage, vice can refer to a fault, a negative character trait, a defect, an infirmity, or a bad or unhealthy habit (such as an addiction to smoking). Vices are usually associated with a transgression in a person's character or temperament rather than their morality. Synonyms for vice include fault, sin, depravity, iniquity, wickedness, and corruption.

The opposite of vice is virtue.

Etymology

The modern English term that best captures its original meaning is the word vicious, which means "full of vice". In this sense, the word vice comes from the Latin word vitium, meaning "failing or defect".

(This meaning is completely separate from the word vice when used as an official title to indicate a deputy, substitute or subordinate, as in vice president, vice-chancellor or viceroy. The etymology of this usage derives from the Latin prefix vice-, meaning "in the place of".)