Concept
Cube
Overview
A cube is a three-dimensional solid object in geometry. It has eight vertices and twelve straight edges of the same length, so that these edges form six square faces of the same size. It is an example of a polyhedron. It is a special case of a cuboid, a parallelepiped, and a rhombohedron in which all six quadrilateral faces are squares. It is a three-dimensional hypercube, a family of polytopes that also includes the two-dimensional square and four-dimensional tesseract.
The cube is found in many popular cultures, including toys and games, the arts, optical illusions, and architectural buildings. Cubes can be found in crystal structures, science, and technological devices. It is also found in ancient texts, such as Plato's work Timaeus, which described a set of solids now called Platonic solids, associating a cube with the classical element of earth. A cube with unit length is the canonical unit of volume in three-dimensional space, relative to which other solid objects are measured.
The cube can be represented in many ways. One of them is by drawing a graph with vertices connected with an edge in a plane. Such a graph is called the cubical graph, a special case of the hypercube graph.
The cube is the core of many polyhedra's construction or other geometrical shapes. For example, truncating a cube's vertices results in a truncated cube. Joining one or more cubes face-to-face yields a polycube, a three-dimensional version of polyominoes. Two or more cubes can have the same centre, forming polyhedral compounds. Cubes can form a honeycomb by attaching face-to-face, filling a space without leaving a gap.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
In the original texts
Passages from public-domain books where Cube is discussed.
Let us now assign the geometrical forms to their respective elements. The cube is the most stable of them because resting on a quadrangular plane surface, and composed of isosceles triangles. To the earth then, which is the most stable of bodies and the most easily modelled of them, may be assigned the form of a cube; and the remaining forms to the other elements,—to fire the pyramid, to air the octahedron, and to…
Plato, Timaeus
states what it is; names the idea; author linked in the graph
the secretion began to decrease, and after 48 hrs. the glands were left dry; but very minute bits of albumen were still left undissolved. (5) Smaller cubes of albumen (about 1/50 or 1/60 of an inch, .508 or .423 mm.) were placed on four glands; after 18 hrs. one cube was completely dissolved, the others being much reduced in size, softened, and transparent. After 24 hrs. two of the cubes were completely dissolved…
Charles Darwin, Insectivorous Plants
names the idea; opens on it
To which the acute and judicious proposer answers: ‘Not.’ For, though he has obtained the experience of how a globe, how a cube affects his touch; yet he has not obtained the experience that what affects his touch so and so, must affect his sight so and so; so that a protuberant angle in the cube, that pressed his hand unequally, shall appear to his eye as it does in the cube.—I agree with this thinking gentleman…
George Berkeley, The Works of George Berkeley. Vol. 1 of 4
names the idea; opens on it
For though he has obtained the experience of how a globe, how a cube, affects his touch, yet he has not yet attained the experience that what affects his touch so or so must affect his sight so or so: or that a protuberant angle in the cube that pressed his hand unequally shall appear to his eye as it doth in the cube." I agree with this thinking gentleman, whom I am proud to call my friend, in his answer to this…
George Berkeley, An Essay Towards a New Theory of Vision
names the idea; opens on it
Now geometrically regular figures, such as a circle, a square, a cube, etc., are commonly adduced by critics of taste as the simplest and most indisputable examples of beauty; and yet they are called regular, because we can only represent them by regarding them as mere presentations of a definite concept which prescribes the rule for the figure (according to which alone it is possible). One of these two must be…
Immanuel Kant, Kant's Critique of Judgement
states what it is; opens on it; names the idea
Related ideas
- Golden ratio
- Harmonice Mundi
- Johannes Kepler
- Geometry
- Mercury (planet)
- Planet
- Plato
- Euclid's Elements
- Quantum mechanics
- Robert A. Heinlein
- Pythagorean theorem
- Solar System
- Wave
- Gravity
- Salvador Dalí
- Timaeus (dialogue)
- Classical element
- Earth (classical element)
- Atom
- Earth
- Euclid
- Ernst Haeckel
- Mysterium Cosmographicum
Place in the tradition
Part of Pythagoreanism.