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In geometry, a tesseract or 4-cube is a four-dimensional hypercube, analogous to a two-dimensional square and a three-dimensional cube. [1] Just as the perimeter of the square consists of four edges and the surface of the cube consists of six square faces, the hypersurface of the tesseract consists of eight cubical cells, meeting at right angles.
In geometry, a hypercube is an n-dimensional analogue of a square (n = 2) and a cube (n = 3); the special case for n = 4 is known as a tesseract.It is a closed, compact, convex figure whose 1-skeleton consists of groups of opposite parallel line segments aligned in each of the space's dimensions, perpendicular to each other and of the same length.
Four-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space (3D). Three-dimensional space is the simplest possible abstraction of the observation that one needs only three numbers, called dimensions, to describe the sizes or locations of objects in the everyday world.
The Fourth Dimension teaches readers about the concept of a fourth spatial dimension. Several analogies are made to Flatland; in particular, Rucker compares how a square in Flatland would react to a cube in Spaceland to how a cube in Spaceland would react to a hypercube from the fourth dimension. The book also includes multiple puzzles.
The Fourth Dimension (4D) was a major video game publisher for the BBC Micro, Acorn Electron, Acorn Archimedes and RiscPC between 1989 and 1998. Previously, The Fourth Dimension had been known as Impact Software , which specialised mainly in BBC Micro games.
A hypercube n H m with numbers in the analytical numberrange [0..m n-1] has the magic sum: n S m = m (m n - 1) / 2. Besides more specific qualifications the following are the most important, "summing" of course stands for "summing correctly to the magic sum" {r-agonal} : all main (unbroken) r-agonals are summing.