Книга: Abstract polytope: Mathematics, Combinatorics, Polytope, Euclidean space, Polygon, Polyhedron, 11-cell, 57-cell, Regular polytope, Graded poset

In mathematics, an abstract polytope, informally speaking, is a structure which considers only the combinatorial properties of a traditional polytope, ignoring many of its other properties, such as angles, edge lengths, etc.. No concept of space, such as Euclidean space, is required to contain it. The term polytope is a generalisation of polygons and polyhedra into any number of dimensions. A formal definition of an abstract polytope is given below. In fact, this definition is more general than the traditional concept of a polytope, and allows many new objects that have no counterpart in traditional theory. Throughout this article, polytope means abstract polytope, unless stated otherwise. The term traditional will be used, without being formally defined here, to refer to what is generally understood by polytope, excluding abstract polytopes. Some authors also use the terms classical or geometric.