Types of Polytopes

Generally, three types of polytopes are:

• Infinite Polytopes
• Abstract Polytopes
• Complex Polytopes

Infinite Polytopes

An infinite polytope is a generalization of the concept of a polytope, which is a higher-dimensional analogue of a polygon in two dimensions or a polyhedron in three dimensions. Image added below shows an Infinite Polytopes.

Abstract Polytope

An abstract polytope is a geometric construct that generalizes the notion of a regular polytope in Euclidean space to higher ranks and dimensions, including dimensions beyond the traditional three-dimensional space we are familiar with. Image added below shows an Abstract Polytopes.

Complex Polytope

A complex polytope is a generalization of the concept of a regular polytope to the complex number plane. Just as a regular polytope in Euclidean space is defined by its vertices and bounded by flat faces, a complex polytope is defined by its vertices in the complex plane and bounded by complex lines or complex circles. Image added below shows an Complex Polytopes.

Polytopes are defined as objects with flat sides (faces) in geometry. Polytopes are the generalization of three-dimensional polyhedra to any number of dimensions.

Polytope is a partition of Euclidean space, resulting in a polytope filling a large portion. A regular polytope is generally of platonic form at arbitrary levels. The Swiss mathematician Ludwig Schläfli discovered the regular polytope Ludwig Schläflias as early as 1852.

In this article, we have covered the Polytope definition, types, examples and others in detail.