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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. 

## Aerodrome

An aerodrome (Commonwealth English) or airdrome (American English) is a location from which aircraft flight operations take place, regardless of whether they involve air cargo, passengers, or neither.

## Aerodynamics

Aerodynamics, from Greek ἀήρ aer (air) + δυναμική (dynamics), is the study of the motion of air, particularly its interaction with a solid object, such as an airplane wing.

## Alternating group

In mathematics, an alternating group is the group of even permutations of a finite set.

## Alternation (geometry)

In geometry, an alternation or partial truncation, is an operation on a polygon, polyhedron, tiling, or higher dimensional polytope that removes alternate vertices.

## American Mathematical Monthly

The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894.

## Ammonium

The ammonium cation is a positively charged polyatomic ion with the chemical formula.

## Antiprism

In geometry, an n-sided antiprism is a polyhedron composed of two parallel copies of some particular n-sided polygon, connected by an alternating band of triangles.

## Apex (geometry)

In geometry, an apex (Latin for 'summit, peak, tip, top, extreme end') is the vertex which is in some sense the "highest" of the figure to which it belongs.

## Approximation

An approximation is anything that is similar but not exactly equal to something else.

## Area

Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane.

## Aristotle

Aristotle (Ἀριστοτέλης Aristotélēs,; 384–322 BC) was an ancient Greek philosopher and scientist born in the city of Stagira, Chalkidiki, in the north of Classical Greece.

## Artificial intelligence

Artificial intelligence (AI, also machine intelligence, MI) is intelligence demonstrated by machines, in contrast to the natural intelligence (NI) displayed by humans and other animals.

## Base (geometry)

In geometry, a base is a side of a polygon or a face of a polyhedron, particularly one oriented perpendicular to the direction in which height is measured, or on what is considered to be the "bottom" of the figure.

## Bisection

In geometry, bisection is the division of something into two equal or congruent parts, usually by a line, which is then called a bisector.

## Boerdijk–Coxeter helix

The Boerdijk–Coxeter helix, named after H. S. M. Coxeter and A. H. Boerdijk, is a linear stacking of regular tetrahedra, arranged so that the edges of the complex that belong to only one tetrahedron form three intertwined helices.

## Caltrop

A caltrop (also known as caltrap, galtrop, cheval trap, galthrap, galtrap, calthrop, jackrock or crow's footBattle of Alesia (Caesar's conquest of Gaul in 52 BC)), Battlefield Detectives program, (2006), rebroadcast: 2008-09-08 on History Channel International (13;00-14:00 hrs EDST); Note: No mention of name caltrop at all, but illustrated and given as battle key to defend Roman lines of circumvaliation per recent digs evidence.

## Cartesian coordinate system

A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.

## Central angle

Central angles are subtended by an arc between those two points, and the arc length is the central angle of a circle of radius one (measured in radians).

## Centroid

In mathematics and physics, the centroid or geometric center of a plane figure is the arithmetic mean position of all the points in the shape.

## Cevian

In geometry, a cevian is any line segment in a triangle with one endpoint on a vertex of the triangle and the other endpoint on the opposite side.

## Chemical engineering

Chemical engineering is a branch of engineering that uses principles of chemistry, physics, mathematics and economics to efficiently use, produce, transform, and transport chemicals, materials and energy.

## Circumscribed sphere

In geometry, a circumscribed sphere of a polyhedron is a sphere that contains the polyhedron and touches each of the polyhedron's vertices.

## Civil engineering

Civil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including works such as roads, bridges, canals, dams, airports, sewerage systems, pipelines, and railways.

## Commandino's theorem

Commandino's theorem, named after Federico Commandino (1509–1575), states that the four medians of a tetrahedron are concurrent at a point S, which divides them in a 3:1 ratio.

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## Compound of five tetrahedra

The compound of five tetrahedra is one of the five regular polyhedral compounds.

## Compound of ten tetrahedra

The compound of ten tetrahedra is one of the five regular polyhedral compounds.

## Compound of two tetrahedra

In geometry, a compound of two tetrahedra is constructed by two overlapping tetrahedra, usually implied as regular tetrahedra.

## Computational fluid dynamics

Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to solve and analyze problems that involve fluid flows.

## Concurrent lines

In geometry, three or more lines in a plane or higher-dimensional space are said to be concurrent if they intersect at a single point.

## Conformal map

In mathematics, a conformal map is a function that preserves angles locally.

## Congruence (geometry)

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

## Conjugacy class

In mathematics, especially group theory, the elements of any group may be partitioned into conjugacy classes; members of the same conjugacy class share many properties, and study of conjugacy classes of non-abelian groups reveals many important features of their structure.

## 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.

## Covalent bond

A covalent bond, also called a molecular bond, is a chemical bond that involves the sharing of electron pairs between atoms.

## Coxeter element

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

## Coxeter notation

In geometry, Coxeter notation (also Coxeter symbol) is a system of classifying symmetry groups, describing the angles between with fundamental reflections of a Coxeter group in a bracketed notation expressing the structure of a Coxeter-Dynkin diagram, with modifiers to indicate certain subgroups.

## Coxeter–Dynkin diagram

In geometry, a Coxeter–Dynkin diagram (or Coxeter diagram, Coxeter graph) is a graph with numerically labeled edges (called branches) representing the spatial relations between a collection of mirrors (or reflecting hyperplanes).

## Cross product

In mathematics and vector algebra, the cross product or vector product (occasionally directed area product to emphasize the geometric significance) is a binary operation on two vectors in three-dimensional space \left(\mathbb^3\right) and is denoted by the symbol \times.

## Crystal

A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions.

## 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.

## Cyclic group

In algebra, a cyclic group or monogenous group is a group that is generated by a single element.

## Degrees of freedom (statistics)

In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary.

## Demihypercube

In geometry, demihypercubes (also called n-demicubes, n-hemicubes, and half measure polytopes) are a class of n-polytopes constructed from alternation of an n-hypercube, labeled as h&gamma;n for being half of the hypercube family, &gamma;n.

## Determinant

In linear algebra, the determinant is a value that can be computed from the elements of a square matrix.

## Dice

Dice (singular die or dice; from Old French dé; from Latin datum "something which is given or played") are small throwable objects with multiple resting positions, used for generating random numbers.

## Digon

In geometry, a digon is a polygon with two sides (edges) and two vertices.

## Dihedral angle

A dihedral angle is the angle between two intersecting planes.

## Disphenoid

In geometry, a disphenoid (from Greek sphenoeides, "wedgelike") is a tetrahedron whose four faces are congruent acute-angled triangles.

## Distance geometry problem

The distance geometry problem is that of characterization and study of sets of points based only on given values of the distances between member pairs.

## Distance-regular graph

In mathematics, a distance-regular graph is a regular graph such that for any two vertices v and w, the number of vertices at distance j from v and at distance k from w depends only upon j, k, and i.

## Distance-transitive graph

In the mathematical field of graph theory, a distance-transitive graph is a graph such that, given any two vertices v and w at any distance i, and any other two vertices x and y at the same distance, there is an automorphism of the graph that carries v to x and w to y.

## Dodecahedron

In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα dōdeka "twelve" + ἕδρα hédra "base", "seat" or "face") is any polyhedron with twelve flat faces.

## Dot product

In mathematics, the dot product or scalar productThe term scalar product is often also used more generally to mean a symmetric bilinear form, for example for a pseudo-Euclidean space.

## 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.

## Edge (geometry)

In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.

## Electromagnetic field

An electromagnetic field (also EMF or EM field) is a physical field produced by electrically charged objects.

## Elliptic geometry

Elliptic geometry is a geometry in which Euclid's parallel postulate does not hold.

## Equilateral triangle

In geometry, an equilateral triangle is a triangle in which all three sides are equal.

## Euclidean geometry

Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.

## Euler line

In geometry, the Euler line, named after Leonhard Euler, is a line determined from any triangle that is not equilateral.

## Exsphere (polyhedra)

In geometry, the exsphere of a face of a regular polyhedron is the sphere outside the polyhedron which touches the face and the planes defined by extending the adjacent faces outwards.

## 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.

## Finite element method

The finite element method (FEM), is a numerical method for solving problems of engineering and mathematical physics.

## Flexagon

In geometry, flexagons are flat models, usually constructed by folding strips of paper, that can be flexed or folded in certain ways to reveal faces besides the two that were originally on the back and front.

## Fluorescent lamp

A fluorescent lamp, or fluorescent tube, is a low-pressure mercury-vapor gas-discharge lamp that uses fluorescence to produce visible light.

## Forum Geometricorum

Forum Geometricorum: A Journal on Classical Euclidean Geometry (often abbreviated Forum Geom.) is a peer-reviewed open-access academic journal that specializes in mathematical research papers on Euclidean geometry.

## Four-sided die

Four-sided dice, abbreviated d4, are often used in tabletop role-playing games to obtain random integers in the range 1–4.

## Futurama

Futurama is an American animated sitcom created by Matt Groening for the Fox Broadcasting Company.

## Gaspard Monge

Gaspard Monge, Comte de Péluse (9 May 1746 – 28 July 1818) was a French mathematician, the inventor of descriptive geometry (the mathematical basis of technical drawing), and the father of differential geometry.

## 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.

## Graph (discrete mathematics)

In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".

## Graph theory

In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.

## HAL 9000

HAL 9000 is a fictional character and the main antagonist in Arthur C. Clarke's Space Odyssey series.

## Hamiltonian path

In the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once.

## Handedness

In human biology, handedness is a better, faster, or more precise performance or individual preference for use of a hand, known as the dominant hand; the less capable or less preferred hand is called the non-dominant hand.

## Harold Scott MacDonald Coxeter

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

## Heron's formula

In geometry, Heron's formula (sometimes called Hero's formula), named after Hero of Alexandria, gives the area of a triangle by requiring no arbitrary choice of side as base or vertex as origin, contrary to other formulae for the area of a triangle, such as half the base times the height or half the norm of a cross product of two sides.

## Hill tetrahedron

In geometry, the Hill tetrahedra are a family of space-filling tetrahedra.

## Honeycomb (geometry)

In geometry, a honeycomb is a space filling or close packing of polyhedral or higher-dimensional cells, so that there are no gaps.

## Hyperbolic space

In mathematics, hyperbolic space is a homogeneous space that has a constant negative curvature, where in this case the curvature is the sectional curvature.

## Incircle and excircles of a triangle

In geometry, the incircle or inscribed circle of a triangle is the largest circle contained in the triangle; it touches (is tangent to) the three sides.

## Inscribed sphere

In geometry, the inscribed sphere or insphere of a convex polyhedron is a sphere that is contained within the polyhedron and tangent to each of the polyhedron's faces.

## K-vertex-connected graph

In graph theory, a connected graph G is said to be k-vertex-connected (or k-connected) if it has more than k vertices and remains connected whenever fewer than k vertices are removed.

## Klein four-group

In mathematics, the Klein four-group (or just Klein group or Vierergruppe, four-group, often symbolized by the letter V or as K4) is the group, the direct product of two copies of the cyclic group of order 2.

## Law of cosines

In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles.

## Law of sines

In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of a triangle (any shape) to the sines of its angles.

## List of finite spherical symmetry groups

Finite spherical symmetry groups are also called point groups in three dimensions.

## Lone pair

In chemistry, a lone pair refers to a pair of valence electrons that are not shared with another atomIUPAC Gold Book definition: and is sometimes called a non-bonding pair.

## Martina Schettina

Martina Schettina (born 1961) is an Austrian artist.

## Marvin Minsky

Marvin Lee Minsky (August 9, 1927 – January 24, 2016) was an American cognitive scientist concerned largely with research of artificial intelligence (AI), co-founder of the Massachusetts Institute of Technology's AI laboratory, and author of several texts concerning AI and philosophy.

## Mathematics Magazine

Mathematics Magazine is a refereed bimonthly publication of the Mathematical Association of America.

## Median (geometry)

In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposing side, bisecting it.

## Methane

Methane is a chemical compound with the chemical formula (one atom of carbon and four atoms of hydrogen).

## Midsphere

In geometry, the midsphere or intersphere of a polyhedron is a sphere which is tangent to every edge of the polyhedron.

## Mirror image

A mirror image (in a plane mirror) is a reflected duplication of an object that appears almost identical, but is reversed in the direction perpendicular to the mirror surface.

## Monolith (Space Odyssey)

In Arthur C. Clarke's Space Odyssey, Monoliths are machines built by an unseen extraterrestrial species.

## Mudvayne

Mudvayne was an American heavy metal band from Peoria, Illinois formed in 1996.

## Murakami–Yano formula

In geometry, the Murakami–Yano formula, introduced by, is a formula for the volume of a hyperbolic or spherical tetrahedron given in terms of its dihedral angles.

## N-skeleton

In mathematics, particularly in algebraic topology, the of a topological space X presented as a simplicial complex (resp. CW complex) refers to the subspace Xn that is the union of the simplices of X (resp. cells of X) of dimensions In other words, given an inductive definition of a complex, the is obtained by stopping at the.

## Naval architecture

Naval architecture, or naval engineering, along with automotive engineering and aerospace engineering, is an engineering discipline branch of vehicle engineering, incorporating elements of mechanical, electrical, electronic, software and safety engineering as applied to the engineering design process, shipbuilding, maintenance, and operation of marine vessels and structures.

## 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.

## Niccolò Fontana Tartaglia

Niccolò Fontana Tartaglia (1499/1500, Brescia &ndash; 13 December 1557, Venice) was a Venetian mathematician, engineer (designing fortifications), a surveyor (of topography, seeking the best means of defense or offense) and a bookkeeper from the then-Republic of Venice (now part of Italy).

## Nine-point circle

In geometry, the nine-point circle is a circle that can be constructed for any given triangle.

## Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).

## Oblivion (2013 film)

Oblivion is a 2013 American post-apocalyptic science fiction film based on Joseph Kosinski's unpublished graphic novel of the same name.

## Octahedron

In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces, twelve edges, and six vertices.

## Orbifold notation

In geometry, orbifold notation (or orbifold signature) is a system, invented by William Thurston and popularized by the mathematician John Conway, for representing types of symmetry groups in two-dimensional spaces of constant curvature.

## Orbital hybridisation

In chemistry, orbital hybridisation (or hybridization) is the concept of mixing atomic orbitals into new hybrid orbitals (with different energies, shapes, etc., than the component atomic orbitals) suitable for the pairing of electrons to form chemical bonds in valence bond theory.

## Origami

) is the art of paper folding, which is often associated with Japanese culture.

## Orthocentric tetrahedron

In geometry, an orthocentric tetrahedron is a tetrahedron where all three pairs of opposite edges are perpendicular.

## Orthographic projection

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

## Parallelepiped

In geometry, a parallelepiped is a three-dimensional figure formed by six parallelograms (the term rhomboid is also sometimes used with this meaning).

## Partial differential equation

In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.

## Perpendicular

In elementary geometry, the property of being perpendicular (perpendicularity) is the relationship between two lines which meet at a right angle (90 degrees).

## Phase diagram

A phase diagram in physical chemistry, engineering, mineralogy, and materials science is a type of chart used to show conditions (pressure, temperature, volume, etc.) at which thermodynamically distinct phases occur and coexist at equilibrium.

## Piero della Francesca

Piero della Francesca (c. 1415 – 12 October 1492) was an Italian painter of the Early Renaissance.

## Planar graph

In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints.

## Plateau's laws

Plateau's laws describe the structure of soap films.

## Platonic graph

In the mathematical field of graph theory, a Platonic graph is a graph that has one of the Platonic solids as its skeleton.

## Platonic solid

In three-dimensional space, a Platonic solid is a regular, convex polyhedron.

## Point groups in three dimensions

In geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a sphere.

## Point reflection

In geometry, a point reflection or inversion in a point (or inversion through a point, or central inversion) is a type of isometry of Euclidean space.

## Polygon

In elementary geometry, a polygon is a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed polygonal chain or circuit.

## Polygon mesh

A polygon mesh is a collection of, s and s that defines the shape of a polyhedral object in 3D computer graphics and solid modeling.

## Polyhedron

In geometry, a polyhedron (plural polyhedra or polyhedrons) is a solid in three dimensions with flat polygonal faces, straight edges and sharp corners or vertices.

## Polytope compound

A polyhedral compound is a figure that is composed of several polyhedra sharing a common centre.

## Projection (linear algebra)

In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that.

## Pyramid (geometry)

In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex.

## Pyraminx

The Pyraminx is a regular tetrahedron puzzle in the style of Rubik's Cube.

## Pyramorphix

The Pyramorphix (often misspelt Pyramorphinx) is a tetrahedral puzzle similar to the Rubik's Cube.

## Quaternions and spatial rotation

Unit quaternions, also known as versors, provide a convenient mathematical notation for representing orientations and rotations of objects in three dimensions.

## Rectangle

In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles.

## Rectification (geometry)

In Euclidean geometry, rectification or complete-truncation is the process of truncating a polytope by marking the midpoints of all its edges, and cutting off its vertices at those points.

## Regular graph

In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency.

## Regular Polytopes (book)

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

## Resistor

A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element.

## Rhombohedron

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

## Right angle

In geometry and trigonometry, a right angle is an angle of exactly 90° (degrees), corresponding to a quarter turn.

## Role-playing

Role-playing is the changing of one's behaviour to assume a role, either unconsciously to fill a social role, or consciously to act out an adopted role.

## Royal Game of Ur

The Royal Game of Ur, also known as the Game of Twenty Squares or simply the Game of Ur, is a two-player strategy race board game that was first played in ancient Mesopotamia during the early third millennium BC.

## Rubik's Cube

Rubik's Cube is a 3-D combination puzzle invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik.

## Schläfli orthoscheme

In geometry, Schläfli orthoscheme is a type of simplex.

## Schläfli symbol

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

## Schoenflies notation

The Schoenflies (or Schönflies) notation, named after the German mathematician Arthur Moritz Schoenflies, is one of two conventions commonly used to describe point groups.

## Semiconductor

A semiconductor material has an electrical conductivity value falling between that of a conductor – such as copper, gold etc.

## Silicon

Silicon is a chemical element with symbol Si and atomic number 14.

## Simplex

In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions.

## Skew lines

In three-dimensional geometry, skew lines are two lines that do not intersect and are not parallel.

## Slope

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

## Solder

Solder (or in North America) is a fusible metal alloy used to create a permanent bond between metal workpieces.

## Solid angle

In geometry, a solid angle (symbol) is a measure of the amount of the field of view from some particular point that a given object covers.

## Solid-state electronics

Solid-state electronics means semiconductor electronics; electronic equipment using semiconductor devices such as semiconductor diodes, transistors, and integrated circuits (ICs).

## Space frame

In architecture and structural engineering, a space frame or space structure is a rigid, lightweight, truss-like structure constructed from interlocking struts in a geometric pattern.

## Spherical polyhedron

In mathematics, a spherical polyhedron or spherical tiling is a tiling of the sphere in which the surface is divided or partitioned by great arcs into bounded regions called spherical polygons.

## Spieker circle

In geometry, the incircle of the medial triangle of a triangle is the Spieker circle, named after 19th-century German geometer Theodor Spieker.

## 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.

## Stanley Kubrick

Stanley Kubrick (July 26, 1928 – March 7, 1999) was an American film director, screenwriter, and producer.

## Stellated octahedron

The stellated octahedron is the only stellation of the octahedron.

No description.

## Stereographic projection

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

## Symmetric graph

In the mathematical field of graph theory, a graph G is symmetric (or arc-transitive) if, given any two pairs of adjacent vertices u1—v1 and u2—v2 of G, there is an automorphism such that In other words, a graph is symmetric if its automorphism group acts transitively upon ordered pairs of adjacent vertices (that is, upon edges considered as having a direction).

## Symmetric group

In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions.

## Symmetry group

In group theory, the symmetry group of an object (image, signal, etc.) is the group of all transformations under which the object is invariant with composition as the group operation.

## Symmetry in mathematics

Symmetry occurs not only in geometry, but also in other branches of mathematics.

## Symmetry number

The symmetry number or symmetry order of an object is the number of different but indistinguishable (or equivalent) arrangements (or views) of the object, i.e. the order of its symmetry group.

## Synergetics (Fuller)

Synergetics is the empirical study of systems in transformation, with an emphasis on total system behavior unpredicted by the behavior of any isolated components, including humanity's role as both participant and observer.

## Table of polyhedron dihedral angles

The dihedral angles for the edge-transitive polyhedra are.

## Tangent

In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point.

## Telecommunications engineering

Telecommunications engineering is an engineering discipline centered on electrical and computer engineering which seeks to support and enhance telecommunication systems.

## Tetra Pak

Tetra Pak is a multinational food packaging and processing sub-company of Tetra Laval, with head offices in Lund, Sweden, and Lausanne, Switzerland.

## Tetragonal disphenoid honeycomb

The tetragonal disphenoid tetrahedral honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space made up of identical tetragonal disphenoidal cells.

## Tetrahedral hypothesis

The tetrahedral hypothesis is an obsolete scientific theory attempting to explain the arrangement of the Earth's continents and oceans by referring to the geometry of a tetrahedron.

## Tetrahedral kite

A tetrahedral kite is a multicelled rigid box kite composed of tetrahedrally shaped cells to create a kind of tetrahedral truss.

## Tetrahedral molecular geometry

In a tetrahedral molecular geometry, a central atom is located at the center with four substituents that are located at the corners of a tetrahedron.

## Tetrahedral number

A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedron.

## Tetrahedral-octahedral honeycomb

The tetrahedral-octahedral honeycomb, alternated cubic honeycomb is a quasiregular space-filling tessellation (or honeycomb) in Euclidean 3-space.

## 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.

## Tetrahedron (journal)

Tetrahedron is a weekly peer-reviewed scientific journal covering the field of organic chemistry.

## Tetrahedron packing

In geometry, tetrahedron packing is the problem of arranging identical regular tetrahedra throughout three-dimensional space so as to fill the maximum possible fraction of space.

## The End of All Things to Come

The End of All Things to Come is the second studio album by American heavy metal band Mudvayne.

## Three-dimensional space

Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameters) are required to determine the position of an element (i.e., point).

## Trapezohedron

The n-gonal trapezohedron, antidipyramid, antibipyramid or deltohedron is the dual polyhedron of an n-gonal antiprism.

## Triangle

A triangle is a polygon with three edges and three vertices.

## Triangular bipyramid

In geometry, the triangular bipyramid (or dipyramid) is a type of hexahedron, being the first in the infinite set of face-transitive bipyramids.

## Triple product

In vector algebra, a branch of mathematics, the triple product is a product of three 3-dimensional vectors, usually Euclidean vectors.

## Trirectangular tetrahedron

In geometry, a trirectangular tetrahedron is a tetrahedron where all three face angles at one vertex are right angles.

## Trivial group

In mathematics, a trivial group is a group consisting of a single element.

## Uniform polyhedron

A uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other).

## Unit sphere

In mathematics, a unit sphere is the set of points of distance 1 from a fixed central point, where a generalized concept of distance may be used; a closed unit ball is the set of points of distance less than or equal to 1 from a fixed central point.

## Valence (chemistry)

In chemistry, the valence or valency of an element is a measure of its combining power with other atoms when it forms chemical compounds or molecules.

## Vertex (geometry)

In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet.

## Vertex figure

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

## Volume

Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains.

## Wacław Sierpiński

Wacław Franciszek Sierpiński (14 March 1882 – 21 October 1969) was a Polish mathematician.

## Water

Water is a transparent, tasteless, odorless, and nearly colorless chemical substance that is the main constituent of Earth's streams, lakes, and oceans, and the fluids of most living organisms.

## Wedge (geometry)

In solid geometry, a wedge is a polyhedron defined by two triangles and three trapezoid faces.

## Wheel graph

In the mathematical discipline of graph theory, a wheel graph is a graph formed by connecting a single universal vertex to all vertices of a cycle.

## William Lowthian Green

William Lowthian Green (13 September 1819 – 7 December 1890) was an English adventurer and merchant who later became cabinet minister in the Kingdom of Hawaii.

## 2001: A Space Odyssey (film)

2001: A Space Odyssey is a 1968 epic science fiction film produced and directed by Stanley Kubrick.

## 5-cell

In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells.

## References

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