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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.
Norman Johnson advocated the names n-cell, or pentachoron, hexadecachoron, tesseract or octachoron, icositetrachoron, hexacosichoron, and hecatonicosachoron (or dodecacontachoron), coining the term polychoron being a 4D analogy to the 3D polyhedron, and 2D polygon, expressed from the Greek roots poly ("many") and choros ("room" or "space").
The most familiar 4-polytope is the tesseract or hypercube, the 4D analogue of the cube. The convex regular 4-polytopes can be ordered by size as a measure of 4-dimensional content (hypervolume) for the same radius. Each greater polytope in the sequence is rounder than its predecessor, enclosing more content [5] within the same radius. The 4 ...
The Dalí cross, a net of a tesseract The tesseract can be unfolded into eight cubes into 3D space, just as the cube can be unfolded into six squares into 2D space.. In geometry, a tesseract or 4-cube is a four-dimensional hypercube, analogous to a two-dimensional square and a three-dimensional cube. [1]
Table of Shapes Section Sub-Section Sup-Section Name Algebraic Curves ¿ Curves ¿ Curves: Cubic Plane Curve: Quartic Plane Curve: Rational Curves: Degree 2: Conic Section(s) Unit Circle: Unit Hyperbola: Degree 3: Folium of Descartes: Cissoid of Diocles: Conchoid of de Sluze: Right Strophoid: Semicubical Parabola: Serpentine Curve: Trident ...
Net. In four-dimensional geometry, the 24-cell is the convex regular 4-polytope [1] (four-dimensional analogue of a Platonic solid) with Schläfli symbol {3,4,3}. It is also called C 24, or the icositetrachoron, [2] octaplex (short for "octahedral complex"), icosatetrahedroid, [3] octacube, hyper-diamond or polyoctahedron, being constructed of octahedral cells.
In geometry, the 5-cell is the convex 4-polytope with Schläfli symbol {3,3,3}. It is a 5-vertex four-dimensional object bounded by five tetrahedral cells. It is also known as a C 5, hypertetrahedron, pentachoron, [1] pentatope, pentahedroid, [2] tetrahedral pyramid, or 4-simplex (Coxeter's polytope), [3] the simplest possible convex 4-polytope, and is analogous to the tetrahedron in three ...
A polytope is a geometric object with flat sides, which exists in any general number of dimensions. The following list of polygons, polyhedra and polytopes gives the names of various classes of polytopes and lists some specific examples.