42 relations: Abstract polytope, Complex polygon, Dual polyhedron, Face (geometry), Faceting, Final stellation of the icosahedron, Geometry, Great dodecicosacron, Great dodecicosahedron, Great grand stellated 120-cell, Harold Scott MacDonald Coxeter, Hexagon, Isohedral figure, Isosceles triangle, John Horton Conway, Kepler–Poinsot polyhedron, List of uniform polyhedra, List of uniform polyhedra by Schwarz triangle, Michael S. Longuet-Higgins, Moravian star, Pentagram, Pentagrammic bipyramid, Pentagrammic prism, Platonic solid, Polyhedron, Polytope, Polytope compound, Pope, Prismatic uniform polyhedron, Quadrilateral, Regular 4-polytope, Regular polygon, Regular polyhedron, Regular Polytopes (book), Schläfli symbol, Square, Star domain, Star polygon, Stellation, Uniform polyhedron, Uniform star polyhedron, Vertex figure.
In mathematics, an abstract polytope is an algebraic partially ordered set or poset which captures the combinatorial properties of a traditional polytope, but not any purely geometric properties such as angles, edge lengths, etc.
The term complex polygon can mean two different things.
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 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.
Stella octangula as a faceting of the cube In geometry, faceting (also spelled facetting) is the process of removing parts of a polygon, polyhedron or polytope, without creating any new vertices.
In geometry, the complete or final stellation of the icosahedron is the outermost stellation of the icosahedron, and is "complete" and "final" because it includes all of the cells in the icosahedron's stellation diagram.
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 great dodecicosacron is the dual of the great dodecicosahedron (U50).
In geometry, the great dodecicosahedron is a nonconvex uniform polyhedron, indexed as U63.
In geometry, the great grand stellated 120-cell or great grand stellated polydodecahedron is a regular star 4-polytope with Schläfli symbol, one of 10 regular Schläfli-Hess 4-polytopes.
Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.
In geometry, a hexagon (from Greek ἕξ hex, "six" and γωνία, gonía, "corner, angle") is a six-sided polygon or 6-gon.
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.
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.
In geometry, a Kepler–Poinsot polyhedron is any of four regular star polyhedra.
In geometry, 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).
There are many relationships among the uniform polyhedra.
Michael Selwyn Longuet-Higgins FRS (December 8, 1925 – February 26, 2016) was a mathematician and oceanographer at the Department of Applied Mathematics and Theoretical Physics (DAMTP), Cambridge University, England and Institute for Nonlinear Science, University of California, San Diego, USA.
A Moravian star (Herrnhuter Stern) is an illuminated Advent, Christmas, or Epiphany decoration popular in Germany and in places in America and Europe where there are Moravian congregations.
A pentagram (sometimes known as a pentalpha or pentangle or a star pentagon) is the shape of a five-pointed star drawn with five straight strokes.
In geometry, the pentagrammic bipyramid (or dipyramid) is first of the infinite set of face-transitive star bipyramids containing star polygon arrangement of edges.
In geometry, the pentagrammic prism is one in an infinite set of nonconvex prisms formed by square sides and two regular star polygon caps, in this case two pentagrams.
In three-dimensional space, a Platonic solid is a regular, convex 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.
In elementary geometry, a polytope is a geometric object with "flat" sides.
A polyhedral compound is a figure that is composed of several polyhedra sharing a common centre.
The pope (papa from πάππας pappas, a child's word for "father"), also known as the supreme pontiff (from Latin pontifex maximus "greatest priest"), is the Bishop of Rome and therefore ex officio the leader of the worldwide Catholic Church.
In geometry, a prismatic uniform polyhedron is a uniform polyhedron with dihedral symmetry.
In Euclidean plane geometry, a quadrilateral is a polygon with four edges (or sides) and four vertices or corners.
In mathematics, a regular 4-polytope is a regular four-dimensional polytope.
In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).
A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags.
Regular Polytopes is a mathematical geometry book written by Canadian mathematician Harold Scott MacDonald Coxeter.
In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.
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.
In mathematics, a set S in the Euclidean space Rn is called a star domain (or star-convex set, star-shaped set or radially convex set) if there exists an x0 in S such that for all x in S the line segment from x0 to x is in S. This definition is immediately generalizable to any real or complex vector space.
In geometry, a star polygon is a type of non-convex polygon.
In geometry, stellation is the process of extending a polygon in two dimensions, polyhedron in three dimensions, or, in general, a polytope in n dimensions to form a new figure.
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).
In geometry, a uniform star polyhedron is a self-intersecting uniform polyhedron.
In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.