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Rectified 5-simplexes

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In five-dimensional geometry, a rectified 5-simplex is a convex uniform 5-polytope, being a rectification of the regular 5-simplex. [1]

44 relations: Configuration (polytope), Coxeter element, Coxeter group, Dual polyhedron, Edge (geometry), Emanuel Lodewijk Elte, Face (geometry), Five-dimensional space, Geometry, Harold Scott MacDonald Coxeter, Hyperplane, Intersection (set theory), Isohedral figure, Isosceles triangle, Norman Johnson (mathematician), Octahedron, Orthographic projection, Polyhedral combinatorics, Projection (linear algebra), Pyramid (geometry), Rectification (geometry), Rectified 5-cell, Rectified 6-cubes, Rectified 6-orthoplexes, Stellated octahedron, Stereographic projection, Tetrahedral prism, Tetrahedron, Triangle, Truncated 5-cell, Uniform 5-polytope, Uniform polytope, Vertex (geometry), Vertex figure, Wythoff construction, 1 22 polytope, 2 22 honeycomb, 2 31 polytope, 3 31 honeycomb, 3-3 duoprism, 5-cell, 5-simplex, 6-cube, 6-demicube.

Christmas

Christmas is an annual festival commemorating the birth of Jesus Christ,Martindale, Cyril Charles.

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Christmas and holiday season

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.

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Christmas Eve

Christmas Eve is the evening or entire day before Christmas Day, the festival commemorating the birth of Jesus.

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Christmas traditions

Christmas traditions vary from country to country.

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Configuration (polytope)

In geometry, H. S. M. Coxeter called a regular polytope a special kind of configuration.

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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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Coxeter group

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).

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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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Edge (geometry)

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

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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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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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Five-dimensional space

A five-dimensional space is a space with five dimensions.

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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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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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Hyperplane

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

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Intersection (set theory)

In mathematics, the intersection A ∩ B of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.

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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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Isosceles triangle

In geometry, an isosceles triangle is a triangle that has two sides of equal length.

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New Year

New Year is the time or day at which a new calendar year begins and the calendar's year count increments by one.

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New Year's Day

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.

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New Year's Eve

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.

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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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Octahedron

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

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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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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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Projection (linear algebra)

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

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Pyramid (geometry)

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

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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.

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Rectified 5-cell

In four-dimensional geometry, the rectified 5-cell is a uniform 4-polytope composed of 5 regular tetrahedral and 5 regular octahedral cells.

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Rectified 6-cubes

In six-dimensional geometry, a rectified 6-cube is a convex uniform 6-polytope, being a rectification of the regular 6-cube.

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Rectified 6-orthoplexes

In six-dimensional geometry, a rectified 6-orthoplex is a convex uniform 6-polytope, being a rectification of the regular 6-orthoplex.

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Stellated octahedron

The stellated octahedron is the only stellation of the octahedron.

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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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Tetrahedral prism

In geometry, a tetrahedral prism is a convex uniform 4-polytope.

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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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Triangle

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

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Truncated 5-cell

In geometry, a truncated 5-cell is a uniform 4-polytope (4-dimensional uniform polytope) formed as the truncation of the regular 5-cell.

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Uniform 5-polytope

In geometry, a uniform 5-polytope is a five-dimensional uniform polytope.

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Uniform polytope

A uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform facets.

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Vertex (geometry)

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

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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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Wythoff construction

In geometry, a Wythoff construction, named after mathematician Willem Abraham Wythoff, is a method for constructing a uniform polyhedron or plane tiling.

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1 22 polytope

In 6-dimensional geometry, the 122 polytope is a uniform polytope, constructed from the E6 group.

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2 22 honeycomb

In geometry, the 222 honeycomb is a uniform tessellation of the six-dimensional Euclidean space.

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2 31 polytope

In 7-dimensional geometry, 231 is a uniform polytope, constructed from the E7 group.

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2018

2018 has been designated as the third International Year of the Reef by the International Coral Reef Initiative.

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2019

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.

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3 31 honeycomb

In 7-dimensional geometry, the 331 honeycomb is a uniform honeycomb, also given by Schläfli symbol and is composed of 321 and 7-simplex facets, with 56 and 576 of them respectively around each vertex.

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3-3 duoprism

In geometry of 4 dimensions, a 3-3 duoprism or triangular duoprism, the smallest p-q duoprism, is a 4-polytope resulting from the Cartesian product of two triangles.

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5-cell

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

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5-simplex

In five-dimensional geometry, a 5-simplex is a self-dual regular 5-polytope.

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6-cube

In geometry, a 6-cube is a six-dimensional hypercube with 64 vertices, 192 edges, 240 square faces, 160 cubic cells, 60 tesseract 4-faces, and 12 5-cube 5-faces.

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6-demicube

In geometry, a 6-demicube or demihexteract is a uniform 6-polytope, constructed from a 6-cube (hexeract) with alternated vertices removed.

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Redirects here:

0 22 polytope, 0 31 polytope, Birectified 5-simplex, Birectified hexateron, Rectified 5-simplex, Rectified hexateron.

References

[1] https://en.wikipedia.org/wiki/Rectified_5-simplexes

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