## Table of Contents

38 relations: Angle, Computer graphics, Convex polygon, Convex polytope, Convex set, Cube, Curve, CW complex, Edge (geometry), Euler characteristic, Face (geometry), Geometry, Graph theory, Internal and external angles, Intersection (geometry), Khronos Group, Line (geometry), N-skeleton, Peter McMullen, Point (geometry), Polygon, Polyhedron, Polytope, Princeton University Press, Reflectance, Right angle, Shader, Simplicial complex, Sphere, Tessellation, Two ears theorem, Vertex (computer graphics), Vertex (curve), Vertex (graph theory), Vertex arrangement, Vertex figure, Vertex normal, Vertex pipeline.

- Point (geometry)

## Angle

In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

See Vertex (geometry) and Angle

## Computer graphics

Computer graphics deals with generating images and art with the aid of computers.

See Vertex (geometry) and Computer graphics

## Convex polygon

In geometry, a convex polygon is a polygon that is the boundary of a convex set.

See Vertex (geometry) and Convex polygon

## Convex polytope

A convex polytope is a special case of a polytope, having the additional property that it is also a convex set contained in the n-dimensional Euclidean space \mathbb^n. Vertex (geometry) and convex polytope are polytopes.

See Vertex (geometry) and Convex polytope

## Convex set

In geometry, a subset of a Euclidean space, or more generally an affine space over the reals, is convex if, given any two points in the subset, the subset contains the whole line segment that joins them.

See Vertex (geometry) and Convex set

## Cube

In geometry, a cube is a three-dimensional solid object bounded by six square faces.

See Vertex (geometry) and Cube

## Curve

In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight.

See Vertex (geometry) and Curve

## CW complex

A CW complex (also called cellular complex or cell complex) is a kind of a topological space that is particularly important in algebraic topology.

See Vertex (geometry) and CW complex

## Edge (geometry)

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

See Vertex (geometry) and Edge (geometry)

## Euler characteristic

In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent.

See Vertex (geometry) and Euler characteristic

## Face (geometry)

In solid geometry, a face is a flat surface (a planar region) that forms part of the boundary of a solid object; a three-dimensional solid bounded exclusively by faces is a polyhedron.

See Vertex (geometry) and Face (geometry)

## Geometry

Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures.

See Vertex (geometry) and Geometry

## Graph theory

In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.

See Vertex (geometry) and Graph theory

## Internal and external angles

In geometry, an angle of a polygon is formed by two adjacent sides.

See Vertex (geometry) and Internal and external angles

## Intersection (geometry)

In geometry, an intersection is a point, line, or curve common to two or more objects (such as lines, curves, planes, and surfaces).

See Vertex (geometry) and Intersection (geometry)

## Khronos Group

The Khronos Group, Inc. is an open, non-profit, member-driven consortium of 170 organizations developing, publishing and maintaining royalty-free interoperability standards for 3D graphics, virtual reality, augmented reality, parallel computation, vision acceleration and machine learning.

See Vertex (geometry) and Khronos Group

## Line (geometry)

In geometry, a straight line, usually abbreviated line, is an infinitely long object with no width, depth, or curvature, an idealization of such physical objects as a straightedge, a taut string, or a ray of light.

See Vertex (geometry) and Line (geometry)

## N-skeleton

In mathematics, particularly in algebraic topology, the of a topological space presented as a simplicial complex (resp. CW complex) refers to the subspace that is the union of the simplices of (resp. cells of) of dimensions In other words, given an inductive definition of a complex, the is obtained by stopping at the.

See Vertex (geometry) and N-skeleton

## Peter McMullen

Peter McMullen (born 11 May 1942) is a British mathematician, a professor emeritus of mathematics at University College London.

See Vertex (geometry) and Peter McMullen

## Point (geometry)

In geometry, a point is an abstract idealization of an exact position, without size, in physical space, or its generalization to other kinds of mathematical spaces.

See Vertex (geometry) and Point (geometry)

## Polygon

In geometry, a polygon is a plane figure made up of line segments connected to form a closed polygonal chain.

See Vertex (geometry) and Polygon

## Polyhedron

In geometry, a polyhedron (polyhedra or polyhedrons) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices.

See Vertex (geometry) and Polyhedron

## Polytope

In elementary geometry, a polytope is a geometric object with flat sides (faces). Vertex (geometry) and polytope are polytopes.

See Vertex (geometry) and Polytope

## Princeton University Press

Princeton University Press is an independent publisher with close connections to Princeton University.

See Vertex (geometry) and Princeton University Press

## Reflectance

The reflectance of the surface of a material is its effectiveness in reflecting radiant energy.

See Vertex (geometry) and Reflectance

## Right angle

In geometry and trigonometry, a right angle is an angle of exactly 90 degrees or radians corresponding to a quarter turn.

See Vertex (geometry) and Right angle

## Shader

In computer graphics, a shader is a computer program that calculates the appropriate levels of light, darkness, and color during the rendering of a 3D scene—a process known as shading.

See Vertex (geometry) and Shader

## Simplicial complex

In mathematics, a simplicial complex is a set composed of points, line segments, triangles, and their ''n''-dimensional counterparts (see illustration).

See Vertex (geometry) and Simplicial complex

## Sphere

A sphere (from Greek) is a geometrical object that is a three-dimensional analogue to a two-dimensional circle.

See Vertex (geometry) and Sphere

## Tessellation

A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps. Vertex (geometry) and tessellation are polytopes.

See Vertex (geometry) and Tessellation

## Two ears theorem

In geometry, the two ears theorem states that every simple polygon with more than three vertices has at least two ears, vertices that can be removed from the polygon without introducing any crossings.

See Vertex (geometry) and Two ears theorem

## Vertex (computer graphics)

A vertex (plural vertices) in computer graphics is a data structure that describes certain attributes, like the position of a point in 2D or 3D space, or multiple points on a surface.

See Vertex (geometry) and Vertex (computer graphics)

## Vertex (curve)

In the geometry of plane curves, a vertex is a point of where the first derivative of curvature is zero.

See Vertex (geometry) and Vertex (curve)

## Vertex (graph theory)

In discrete mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph consists of a set of vertices and a set of arcs (ordered pairs of vertices).

See Vertex (geometry) and Vertex (graph theory)

## Vertex arrangement

In geometry, a vertex arrangement is a set of points in space described by their relative positions. Vertex (geometry) and vertex arrangement are polytopes.

See Vertex (geometry) and Vertex arrangement

## Vertex figure

In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off. Vertex (geometry) and vertex figure are polytopes.

See Vertex (geometry) and Vertex figure

## Vertex normal

In the geometry of computer graphics, a vertex normal at a vertex of a polyhedron is a directional vector associated with a vertex, intended as a replacement to the true geometric normal of the surface.

See Vertex (geometry) and Vertex normal

## Vertex pipeline

The function of the vertex pipeline in any GPU is to take geometry data (usually supplied as vector points), work with it if needed with either fixed function processes (earlier DirectX), or a vertex shader program (later DirectX), and create all of the 3D data points in a scene to a 2D plane for display on a computer monitor. Vertex (geometry) and vertex pipeline are 3D computer graphics.

See Vertex (geometry) and Vertex pipeline

## See also

### Point (geometry)

- Antipodal point
- Centerpoint (geometry)
- Midpoint
- Orbital node
- Point (geometry)
- Point Cloud Library
- Point in polygon
- Point-set registration
- Point-set triangulation
- Position
- Real point
- Subsolar point
- Vertex (geometry)

## References

Also known as 0-face, Ear (mathematics), Geometric vertex, Mouth (mathematics), Polyhedron vertex, Polytope vertex, Principal vertex.