47 relations: Branko Grünbaum, Catalan solid, Circle packing, Complex polytope, Conway polyhedron notation, Equilateral triangle, Euclidean tilings by convex regular polygons, Geometry, Harold Scott MacDonald Coxeter, Hexagon, Hexagonal tiling, Hyperbolic space, Icosahedron, Isogonal figure, Isogrid, Isohedral figure, Isosceles triangle, John Horton Conway, Kissing number problem, List of convex uniform tilings, Octahedron, Pentakis dodecahedron, Platonic solid, Polyhedron, Pyramid (geometry), Regular Polytopes (book), Right triangle, Schläfli symbol, Simplectic honeycomb, Square tiling, Tessellation, Tetrahedron, Tetrakis hexahedron, Tetrakis square tiling, Triakis tetrahedron, Triangle, Triangular tiling honeycomb, Truncated hexagonal tiling, Truncated order-7 triangular tiling, Truncated trihexagonal tiling, Two-dimensional space, Uniform coloring, Uniform polyhedron, Uniform tiling, Vertex arrangement, Vertex configuration, Voronoi diagram.
Branko Grünbaum (ברנקו גרונבאום; born 2 October 1929) is a Yugoslavian-born mathematician and a professor emeritus at the University of Washington in Seattle.
In mathematics, a Catalan solid, or Archimedean dual, is a dual polyhedron to an Archimedean solid.
In geometry, circle packing is the study of the arrangement of circles (of equal or varying sizes) on a given surface such that no overlapping occurs and so that all circles touch one another.
In geometry, a complex polytope is a generalization of a polytope in real space to an analogous structure in a complex Hilbert space, where each real dimension is accompanied by an imaginary one.
In geometry, Conway polyhedron notation, invented by John Horton Conway and promoted by George W. Hart, is used to describe polyhedra based on a seed polyhedron modified by various prefix operations.
In geometry, an equilateral triangle is a triangle in which all three sides are equal.
Euclidean plane tilings by convex regular polygons have been widely used since antiquity.
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 hexagon (from Greek ἕξ hex, "six" and γωνία, gonía, "corner, angle") is a six-sided polygon or 6-gon.
In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which three hexagons meet at each vertex.
In mathematics, hyperbolic space is a homogeneous space that has a constant negative curvature, where in this case the curvature is the sectional curvature.
In geometry, an icosahedron is a polyhedron with 20 faces.
In geometry, a polytope (a polygon, polyhedron or tiling, for example) is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure.
Isogrid is a type of partially hollowed-out structure formed usually from a single metal plate (or face sheet) with triangular integral stiffening ribs (often called stringers).
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 kissing number is defined as the number of non-overlapping unit spheres that can be arranged such that they each touch another given unit sphere.
This table shows the 11 convex uniform tilings (regular and semiregular) of the Euclidean plane, and their dual tilings.
In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces, twelve edges, and six vertices.
In geometry, a pentakis dodecahedron or kisdodecahedron is a dodecahedron with a pentagonal pyramid covering each face; that is, it is the Kleetope of the dodecahedron.
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 geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex.
Regular Polytopes is a mathematical geometry book written by Canadian mathematician Harold Scott MacDonald Coxeter.
A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree angle).
In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.
In geometry, the simplectic honeycomb (or n-simplex honeycomb) is a dimensional infinite series of honeycombs, based on the _n affine Coxeter group symmetry.
In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane.
A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps.
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.
In geometry, a tetrakis hexahedron (also known as a tetrahexahedron, hextetrahedron, tetrakis cube, and kiscube) is a Catalan solid.
In geometry, the tetrakis square tiling is a tiling of the Euclidean plane.
In geometry, a triakis tetrahedron (or kistetrahedron) is an Archimedean dual solid, or a Catalan solid.
A triangle is a polygon with three edges and three vertices.
The triangular tiling honeycomb is one of 11 paracompact regular space-filling tessellations (or honeycombs) in hyperbolic 3-space.
In geometry, the truncated hexagonal tiling is a semiregular tiling of the Euclidean plane.
In geometry, the Order-7 truncated triangular tiling, sometimes called the hyperbolic soccerball, is a semiregular tiling of the hyperbolic plane.
In geometry, the truncated trihexagonal tiling is one of eight semiregular tilings of the Euclidean plane.
Two-dimensional space or bi-dimensional space is a geometric setting in which two values (called parameters) are required to determine the position of an element (i.e., point).
In geometry, a uniform coloring is a property of a uniform figure (uniform tiling or uniform polyhedron) that is colored to be vertex-transitive.
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 tiling is a tessellation of the plane by regular polygon faces with the restriction of being vertex-transitive.
In geometry, a vertex arrangement is a set of points in space described by their relative positions.
In geometry, a vertex configuration by Walter Steurer, Sofia Deloudi, (2009) pp.
In mathematics, a Voronoi diagram is a partitioning of a plane into regions based on distance to points in a specific subset of the plane.