33 relations: Cartesian coordinate system, Convex polytope, Coxeter group, Coxeter–Dynkin diagram, Cross-polytope, Dual polyhedron, Edge (geometry), Face (geometry), Facet (geometry), Geometry, Gosset–Elte figures, Greek language, Harold Scott MacDonald Coxeter, Hypercube, Icosagon, Norman Johnson (mathematician), Petrie polygon, Projection (linear algebra), Regular polytope, Schläfli symbol, Tetrahedron, Triangle, Uniform 10-polytope, Vertex (geometry), Vertex figure, 10-cube, 5-cell, 5-simplex, 6-simplex, 7-simplex, 8-simplex, 9-orthoplex, 9-simplex.
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.
Christmas is an annual festival commemorating the birth of Jesus Christ,Martindale, Cyril Charles.
The Christmas season, also called the festive season, or the holiday season (mainly in the U.S. and Canada; often simply called the holidays),, is an annually recurring period recognized in many Western and Western-influenced countries that is generally considered to run from late November to early January.
Christmas Eve is the evening or entire day before Christmas Day, the festival commemorating the birth of Jesus.
Christmas traditions vary from country to country.
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.
In mathematics, a Coxeter group, named after H. S. M. Coxeter, is an abstract group that admits a formal description in terms of reflections (or kaleidoscopic mirrors).
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).
In geometry, a cross-polytope, orthoplex, hyperoctahedron, or cocube is a regular, convex polytope that exists in n-dimensions.
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.
In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.
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.
In geometry, a facet is a feature of a polyhedron, polytope, or related geometric structure, generally of dimension one less than the structure itself.
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.
In geometry, the Gosset–Elte figures, named by Coxeter after Thorold Gosset and E. L. Elte, are a group of uniform polytopes which are not regular, generated by a Wythoff construction with mirrors all related by order-2 and order-3 dihedral angles.
Greek (Modern Greek: ελληνικά, elliniká, "Greek", ελληνική γλώσσα, ellinikí glóssa, "Greek language") is an independent branch of the Indo-European family of languages, native to Greece and other parts of the Eastern Mediterranean and the Black Sea.
Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.
In geometry, a hypercube is an ''n''-dimensional analogue of a square and a cube.
In geometry, an icosagon or 20-gon is a twenty-sided polygon.
New Year is the time or day at which a new calendar year begins and the calendar's year count increments by one.
New Year's Day, also called simply New Year's or New Year, is observed on January 1, the first day of the year on the modern Gregorian calendar as well as the Julian calendar.
In the Gregorian calendar, New Year's Eve (also known as Old Year's Day or Saint Sylvester's Day in many countries), the last day of the year, is on 31 December which is the seventh day of Christmastide.
Norman Woodason Johnson (November 12, 1930 – July 13, 2017) was a mathematician, previously at Wheaton College, Norton, Massachusetts.
In geometry, a Petrie polygon for a regular polytope of n dimensions is a skew polygon in which every (n – 1) consecutive sides (but no n) belongs to one of the facets.
In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that.
In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry.
In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.
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.
A triangle is a polygon with three edges and three vertices.
In ten-dimensional geometry, a 10-polytope is a 10-dimensional polytope whose boundary consists of 9-polytope facets, exactly two such facets meeting at each 8-polytope ridge.
In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet.
In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.
In geometry, a 10-cube is a ten-dimensional hypercube.
2018 has been designated as the third International Year of the Reef by the International Coral Reef Initiative.
2019 (MMXIX) will be a common year starting on Tuesday of the Gregorian calendar, the 2019th year of the Common Era (CE) and Anno Domini (AD) designations, the 19th year of the 3rd millennium, the 19th year of the 21st century, and the 10th and last year of the 2010s decade.
In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells.
In five-dimensional geometry, a 5-simplex is a self-dual regular 5-polytope.
In geometry, a 6-simplex is a self-dual regular 6-polytope.
In 7-dimensional geometry, a 7-simplex is a self-dual regular 7-polytope.
In geometry, an 8-simplex is a self-dual regular 8-polytope.
In geometry, a 9-orthoplex or 9-cross polytope, is a regular 9-polytope with 18 vertices, 144 edges, 672 triangle faces, 2016 tetrahedron cells, 4032 5-cells 4-faces, 5376 5-simplex 5-faces, 4608 6-simplex 6-faces, 2304 7-simplex 7-faces, and 512 8-simplex 8-faces.
In geometry, a 9-simplex is a self-dual regular 9-polytope.