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.
In geometry, H. S. M. Coxeter called a regular polytope a special kind of configuration.
In mathematics, the Coxeter number h is the order of a Coxeter element of an irreducible 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).
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.
Emanuel Lodewijk Elte (16 March 1881 in Amsterdam – 9 April 1943 in Sobibór) at joodsmonument.nl was a Dutch mathematician.
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.
A five-dimensional space is a space with five dimensions.
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.
Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.
In geometry, a hyperplane is a subspace whose dimension is one less than that of its ambient space.
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.
In geometry, a polytope of dimension 3 (a polyhedron) or higher is isohedral or face-transitive when all its faces are the same.
In geometry, an isosceles triangle is a triangle that has two sides of equal length.
Norman Woodason Johnson (November 12, 1930 – July 13, 2017) was a mathematician, previously at Wheaton College, Norton, Massachusetts.
In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces, twelve edges, and six vertices.
Orthographic projection (sometimes orthogonal projection), is a means of representing three-dimensional objects in two dimensions.
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.
In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that.
In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex.
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.
In four-dimensional geometry, the rectified 5-cell is a uniform 4-polytope composed of 5 regular tetrahedral and 5 regular octahedral cells.
In six-dimensional geometry, a rectified 6-cube is a convex uniform 6-polytope, being a rectification of the regular 6-cube.
In six-dimensional geometry, a rectified 6-orthoplex is a convex uniform 6-polytope, being a rectification of the regular 6-orthoplex.
The stellated octahedron is the only stellation of the octahedron.
In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane.
In geometry, a tetrahedral prism is a convex uniform 4-polytope.
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 geometry, a truncated 5-cell is a uniform 4-polytope (4-dimensional uniform polytope) formed as the truncation of the regular 5-cell.
In geometry, a uniform 5-polytope is a five-dimensional uniform polytope.
A uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform facets.
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 Wythoff construction, named after mathematician Willem Abraham Wythoff, is a method for constructing a uniform polyhedron or plane tiling.
In 6-dimensional geometry, the 122 polytope is a uniform polytope, constructed from the E6 group.
In geometry, the 222 honeycomb is a uniform tessellation of the six-dimensional Euclidean space.
In 7-dimensional geometry, 231 is a uniform polytope, constructed from the E7 group.
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.
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.
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-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.
In geometry, a 6-demicube or demihexteract is a uniform 6-polytope, constructed from a 6-cube (hexeract) with alternated vertices removed.