26 relations: Balinski's theorem, Convex polytope, Cube, Diagonal, Euler characteristic, Extended side, Face (geometry), Facet (geometry), Geometry, Glossary of graph theory terms, Graduate Texts in Mathematics, Graph theory, K-vertex-connected graph, Line segment, N-skeleton, Planar graph, Polygon, Polyhedron, Polytope, Square, Steinitz's theorem, Tesseract, Triangle, Vertex (geometry), Vertex (graph theory), 4-polytope.

## Balinski's theorem

In polyhedral combinatorics, a branch of mathematics, Balinski's theorem is a statement about the graph-theoretic structure of three-dimensional polyhedra and higher-dimensional polytopes.

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## Convex polytope

A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn.

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## Cube

In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.

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## Diagonal

In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge.

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## 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.

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## Extended side

In plane geometry, an extended side or sideline of a polygon is the line that contains one side of the polygon.

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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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## Facet (geometry)

In geometry, a facet is a feature of a polyhedron, polytope, or related geometric structure, generally of dimension one less than the structure itself.

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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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## Glossary of graph theory terms

This is a glossary of graph theory terms.

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## Graduate Texts in Mathematics

Graduate Texts in Mathematics (GTM) (ISSN 0072-5285) is a series of graduate-level textbooks in mathematics published by Springer-Verlag.

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## Graph theory

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

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## K-vertex-connected graph

In graph theory, a connected graph G is said to be k-vertex-connected (or k-connected) if it has more than k vertices and remains connected whenever fewer than k vertices are removed.

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## Line segment

In geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints.

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## N-skeleton

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

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## Planar graph

In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints.

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## Polygon

In elementary geometry, a polygon is a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed polygonal chain or circuit.

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## 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.

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## Polytope

In elementary geometry, a polytope is a geometric object with "flat" sides.

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## Square

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.

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## Steinitz's theorem

In polyhedral combinatorics, a branch of mathematics, Steinitz's theorem is a characterization of the undirected graphs formed by the edges and vertices of three-dimensional convex polyhedra: they are exactly the (simple) 3-vertex-connected planar graphs (with at least four vertices).

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## Tesseract

In geometry, the tesseract is the four-dimensional analogue of the cube; the tesseract is to the cube as the cube is to the square.

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## Triangle

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

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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 (graph theory)

In 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).

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## 4-polytope

In geometry, a 4-polytope (sometimes also called a polychoron, polycell, or polyhedroid) is a four-dimensional polytope.

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## Redirects here:

1-face, 1-simplex, Polyhedron edge, Polytope edge.