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Tesseract

Index Tesseract

In geometry, the tesseract is the four-dimensional analogue of the cube; the tesseract is to the cube as the cube is to the square. [1]

83 relations: "—And He Built a Crooked House—", A New Era of Thought, American Journal of Mathematics, Ancient Greek, Cartesian product, Charles Howard Hinton, Christian cross variants, Complement graph, Complex polytope, Convex hull, Convex polytope, Coxeter element, Crucifixion (Corpus Hypercubus), Cube, Cuboid, Dihedral angle, Dihedral group, Dissection problem, Dual polyhedron, Duoprism, Emanuel Lodewijk Elte, Euclidean space, Face (geometry), Fez (video game), Four-dimensional space, Geometry, Grande Arche, Graphical projection, Harold Scott MacDonald Coxeter, Hexagonal prism, Hypercube, Hyperplane, Hyperrectangle, Isogonal figure, Isohedral figure, Isotoxal figure, John Horton Conway, Ken Perlin, Klein bottle, Ludwig Schläfli, Macintosh, Matching (graph theory), Mathematics and art, Mathematische Zeitschrift, Möbius strip, Messenger of Mathematics, Microsoft Windows, Nature (journal), Net (polyhedron), Network topology, ..., Norman Johnson (mathematician), Octagon, Orthographic projection, Oxford English Dictionary, Parallel computing, Point at infinity, Polycube, Polyhedral combinatorics, Polytope, Prism (geometry), Rectified tesseract, Regular 4-polytope, Regular polytope, Regular Polytopes (book), Rhombic dodecahedron, Rhombohedron, Robert A. Heinlein, Rudy Rucker, Runcinated 5-cell, Schläfli symbol, Schlegel diagram, Square, Stereographic projection, Stereoscopy, T. Proctor Hall, Tesseractic honeycomb, Tetrahedron, Thorold Gosset, Tree (graph theory), Vertex figure, Victor Schlegel, 16-cell, 3-sphere. Expand index (33 more) »

"—And He Built a Crooked House—"

'—And He Built a Crooked House—' is a science fiction short story by Robert A. Heinlein first published in Astounding Science Fiction in February 1941.

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A New Era of Thought

A New Era of Thought is a non-fiction work written by Charles Howard Hinton, published in 1888 and reprinted in 1900 by Swan Sonnenschein & Co.

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American Journal of Mathematics

The American Journal of Mathematics is a bimonthly mathematics journal published by the Johns Hopkins University Press.

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Ancient Greek

The Ancient Greek language includes the forms of Greek used in ancient Greece and the ancient world from around the 9th century BC to the 6th century AD.

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Cartesian product

In set theory (and, usually, in other parts of mathematics), a Cartesian product is a mathematical operation that returns a set (or product set or simply product) from multiple sets.

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Charles Howard Hinton

Charles Howard Hinton (1853, United Kingdom – 30 April 1907, Washington D.C., United States) was a British mathematician and writer of science fiction works titled Scientific Romances.

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Christian cross variants

This is a list of Christian cross variants.

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Complement graph

In graph theory, the complement or inverse of a graph is a graph on the same vertices such that two distinct vertices of are adjacent if and only if they are not adjacent in.

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Complex polytope

In geometry, a complex polytope is a generalization of a polytope in real space to an analogous structure in a complex Hilbert space, where each real dimension is accompanied by an imaginary one.

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Convex hull

In mathematics, the convex hull or convex envelope or convex closure of a set X of points in the Euclidean plane or in a Euclidean space (or, more generally, in an affine space over the reals) is the smallest convex set that contains X. For instance, when X is a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around X., p. 3.

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Convex polytope

A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn.

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Coxeter element

In mathematics, the Coxeter number h is the order of a Coxeter element of an irreducible Coxeter group.

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Crucifixion (Corpus Hypercubus)

Crucifixion (Corpus Hypercubus) is a 1954 oil-on-canvas painting by Salvador Dalí.

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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.

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Cuboid

In geometry, a cuboid is a convex polyhedron bounded by six quadrilateral faces, whose polyhedral graph is the same as that of a cube.

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Dihedral angle

A dihedral angle is the angle between two intersecting planes.

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Dihedral group

In mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections.

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Dissection problem

In geometry, a dissection problem is the problem of partitioning a geometric figure (such as a polytope or ball) into smaller pieces that may be rearranged into a new figure of equal content.

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Dual polyhedron

In geometry, any polyhedron is associated with a second dual figure, where the vertices of one correspond to the faces of the other and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other.

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Duoprism

In geometry of 4 dimensions or higher, a duoprism is a polytope resulting from the Cartesian product of two polytopes, each of two dimensions or higher.

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Emanuel Lodewijk Elte

Emanuel Lodewijk Elte (16 March 1881 in Amsterdam – 9 April 1943 in Sobibór) at joodsmonument.nl was a Dutch mathematician.

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Euclidean space

In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.

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Face (geometry)

In solid geometry, a face is a flat (planar) surface that forms part of the boundary of a solid object; a three-dimensional solid bounded exclusively by flat faces is a polyhedron.

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Fez (video game)

Fez (stylized as FEZ) is an indie puzzle-platform video game developed by Polytron Corporation and published by Trapdoor.

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Four-dimensional space

A four-dimensional space or 4D space is a mathematical extension of the concept of three-dimensional or 3D space.

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Geometry

Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

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Grande Arche

La Grande Arche de la Défense (also La Grande Arche de la Fraternité) is a monument and building in the business district of La Défense and in the commune of Puteaux, to the west of Paris, France.

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Graphical projection

Graphical projection is a protocol, used in technical drawing, by which an image of a three-dimensional object is projected onto a planar surface without the aid of numerical calculation.

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Harold Scott MacDonald Coxeter

Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.

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Hexagonal prism

In geometry, the hexagonal prism is a prism with hexagonal base.

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Hypercube

In geometry, a hypercube is an ''n''-dimensional analogue of a square and a cube.

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Hyperplane

In geometry, a hyperplane is a subspace whose dimension is one less than that of its ambient space.

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Hyperrectangle

In geometry, an n-orthotopeCoxeter, 1973 (also called a hyperrectangle or a box) is the generalization of a rectangle for higher dimensions, formally defined as the Cartesian product of intervals.

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Isogonal figure

In geometry, a polytope (a polygon, polyhedron or tiling, for example) is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure.

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Isohedral figure

In geometry, a polytope of dimension 3 (a polyhedron) or higher is isohedral or face-transitive when all its faces are the same.

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Isotoxal figure

In geometry, a polytope (for example, a polygon or a polyhedron), or a tiling, is isotoxal or edge-transitive if its symmetries act transitively on its edges.

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John Horton Conway

John Horton Conway FRS (born 26 December 1937) is an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.

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Ken Perlin

Kenneth H. "Ken" Perlin is a professor in the Department of Computer Science at New York University, founding director of the Media Research Lab at NYU, and the Director of the Games for Learning Institute.

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Klein bottle

In topology, a branch of mathematics, the Klein bottle is an example of a non-orientable surface; it is a two-dimensional manifold against which a system for determining a normal vector cannot be consistently defined.

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Ludwig Schläfli

Ludwig Schläfli (15 January 1814 – 20 March 1895) was a Swiss mathematician, specialising in geometry and complex analysis (at the time called function theory) who was one of the key figures in developing the notion of higher-dimensional spaces.

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Macintosh

The Macintosh (pronounced as; branded as Mac since 1998) is a family of personal computers designed, manufactured, and sold by Apple Inc. since January 1984.

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Matching (graph theory)

In the mathematical discipline of graph theory, a matching or independent edge set in a graph is a set of edges without common vertices.

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Mathematics and art

Mathematics and art are related in a variety of ways.

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Mathematische Zeitschrift

Mathematische Zeitschrift (German for Mathematical Journal) is a mathematical journal for pure and applied mathematics published by Springer Verlag.

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Möbius strip

The Möbius strip or Möbius band, also spelled Mobius or Moebius, is a surface with only one side (when embedded in three-dimensional Euclidean space) and only one boundary.

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Messenger of Mathematics

The Messenger of Mathematics is a defunct mathematics journal.

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Microsoft Windows

Microsoft Windows is a group of several graphical operating system families, all of which are developed, marketed, and sold by Microsoft.

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Nature (journal)

Nature is a British multidisciplinary scientific journal, first published on 4 November 1869.

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Net (polyhedron)

In geometry a net of a polyhedron is an arrangement of edge-joined polygons in the plane which can be folded (along edges) to become the faces of the polyhedron.

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Network topology

Network topology is the arrangement of the elements (links, nodes, etc.) of a communication network.

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Norman Johnson (mathematician)

Norman Woodason Johnson (November 12, 1930 – July 13, 2017) was a mathematician, previously at Wheaton College, Norton, Massachusetts.

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Octagon

In geometry, an octagon (from the Greek ὀκτάγωνον oktágōnon, "eight angles") is an eight-sided polygon or 8-gon.

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Orthographic projection

Orthographic projection (sometimes orthogonal projection), is a means of representing three-dimensional objects in two dimensions.

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Oxford English Dictionary

The Oxford English Dictionary (OED) is the main historical dictionary of the English language, published by the Oxford University Press.

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Parallel computing

Parallel computing is a type of computation in which many calculations or the execution of processes are carried out concurrently.

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Point at infinity

In geometry, a point at infinity or ideal point is an idealized limiting point at the "end" of each line.

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Polycube

The seven free tetracubes chiral pentacube Puzzle with a unique solution A polycube is a solid figure formed by joining one or more equal cubes face to face.

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Polyhedral combinatorics

Polyhedral combinatorics is a branch of mathematics, within combinatorics and discrete geometry, that studies the problems of counting and describing the faces of convex polyhedra and higher-dimensional convex polytopes.

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Polytope

In elementary geometry, a polytope is a geometric object with "flat" sides.

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Prism (geometry)

In geometry, a prism is a polyhedron comprising an n-sided polygonal base, a second base which is a translated copy (rigidly moved without rotation) of the first, and n other faces (necessarily all parallelograms) joining corresponding sides of the two bases.

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Rectified tesseract

In geometry, the rectified tesseract, rectified 8-cell is a uniform 4-polytope (4-dimensional polytope) bounded by 24 cells: 8 cuboctahedra, and 16 tetrahedra.

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Regular 4-polytope

In mathematics, a regular 4-polytope is a regular four-dimensional polytope.

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Regular polytope

In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry.

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Regular Polytopes (book)

Regular Polytopes is a mathematical geometry book written by Canadian mathematician Harold Scott MacDonald Coxeter.

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Rhombic dodecahedron

In geometry, the rhombic dodecahedron is a convex polyhedron with 12 congruent rhombic faces.

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Rhombohedron

In geometry, a rhombohedron is a three-dimensional figure like a cube, except that its faces are not squares but rhombi.

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Robert A. Heinlein

Robert Anson Heinlein (See also the biography at the end of For Us, the Living, 2004 edition, p. 261. July 7, 1907 – May 8, 1988) was an American science-fiction writer.

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Rudy Rucker

Rudolf von Bitter Rucker (born March 22, 1946) is an American mathematician, computer scientist, science fiction author, and one of the founders of the cyberpunk literary movement.

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Runcinated 5-cell

In four-dimensional geometry, a runcinated 5-cell is a convex uniform 4-polytope, being a runcination (a 3rd order truncation, up to face-planing) of the regular 5-cell.

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Schläfli symbol

In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.

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Schlegel diagram

In geometry, a Schlegel diagram is a projection of a polytope from R^d into R^ through a point beyond one of its facets or faces.

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Square

In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or (100-gradian angles or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted.

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Stereographic projection

In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane.

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Stereoscopy

Stereoscopy (also called stereoscopics, or stereo imaging) is a technique for creating or enhancing the illusion of depth in an image by means of stereopsis for binocular vision.

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T. Proctor Hall

Thomas Proctor Hall (1858–1931) was a Canadian physician who wrote mathematics, chemistry, physics, theology, and science fiction.

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Tesseractic honeycomb

In four-dimensional euclidean geometry, the tesseractic honeycomb is one of the three regular space-filling tessellations (or honeycombs), represented by Schläfli symbol, and constructed by a 4-dimensional packing of tesseract facets.

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Tetrahedron

In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners.

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Thorold Gosset

John Herbert de Paz Thorold Gosset (16 October 1869 – December 1962) was an English lawyer and an amateur mathematician.

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Tree (graph theory)

In mathematics, and more specifically in graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path.

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Vertex figure

In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.

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Victor Schlegel

Victor Schlegel (1843–1905) was a German mathematician.

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16-cell

In four-dimensional geometry, a 16-cell is a regular convex 4-polytope.

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3-sphere

In mathematics, a 3-sphere, or glome, is a higher-dimensional analogue of a sphere.

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4,3,3, 4-4 duoprism, 4-cube, 4-hypercube, 8-cell, Cubic prism, Octachoron, Regular octachoron, Square duoprism, Teseract, Teserract, Tessaract, Tesseracts, Tesserract, Tetrahedral trapezohedron.

References

[1] https://en.wikipedia.org/wiki/Tesseract

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