In the wide and varied world of Polyhedral complex, there are endless aspects to explore and discover. Whether it's Polyhedral complex itself, its impacts on society, or its evolution over time, there is always something new to learn and reflect on. From its origins to its influence today, Polyhedral complex remains a topic of constant interest and debate. In this article, we will dive into different aspects of Polyhedral complex, exploring its importance, its challenges, and its possible future scenarios. Join us on this exploration and let's discover more about Polyhedral complex together.
In mathematics, a polyhedral complex is a set of polyhedra in a real vector space that fit together in a specific way.[1] Polyhedral complexes generalize simplicial complexes and arise in various areas of polyhedral geometry, such as tropical geometry, splines and hyperplane arrangements.
A polyhedral complex is a set of polyhedra that satisfies the following conditions:
Note that the empty set is a face of every polyhedron, and so the intersection of two polyhedra in may be empty.
A fan is a polyhedral complex in which every polyhedron is a cone from the origin. Examples of fans include: