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The term "4-polytope stubs" does not appear to be a standard term in mathematics or geometry as of my last knowledge update. However, it seems to suggest a focus on properties or structures related to 4-dimensional polytopes (also known as 4-polytopes). A **4-polytope** is a four-dimensional generalization of a polytope, which can be thought of as a shape in four-dimensional space.

In the context of Wikipedia and other online collaborative projects, "polyhedron stubs" refer to short or incomplete articles that provide minimal information about polyhedra, which are three-dimensional geometric shapes with flat faces, straight edges, and vertices. A stub is essentially a starting point for more comprehensive articles, and it marks content that needs expansion and additional detail.

A \(0/1\)-polytope, also known as a \(0/1\)-polyhedron or \(0/1\)-convex hull, is a specific type of convex polytope that is defined by vertices corresponding to binary vectors. More formally, a \(0/1\)-polytope is the convex hull of all points in \(\mathbb{R}^n\) where each coordinate is either 0 or 1.

The 120-cell honeycomb, also known as the 120-cell tessellation or the 120-cell arrangement, is a highly symmetrical geometric structure in four-dimensional space. To understand it better, it's helpful to know some background on polytopes and honeycombs: 1. **Polytopes:** In geometry, a polytope is a generalization of a polygon (in two dimensions) and a polyhedron (in three dimensions) to higher dimensions.

A spherical octahedron is a polyhedral shape that can be inscribed within a sphere. It consists of eight equilateral triangular faces, twelve edges, and six vertices. The concept of great circles arises from spherical geometry, where a great circle is the largest possible circle that can be drawn on a sphere. Great circles are the spherical equivalent of straight lines in plane geometry.

The Adams hemisphere-in-a-square projection is a map projection used for representing the spherical surface of the Earth on a flat surface, specifically designed to preserve the relationships and proportions of areas. This projection is characterized by its ability to contain a hemisphere within a square boundary, which makes it useful for visualizations that require compact representation of large areas. In the Adams projection, the hemisphere is represented in such a way that the edges of the square remain straight, while the curvature of the Earth is taken into account.

An apeirogonal hosohedron is a type of polyhedron that is characterized by having an infinite number of faces, specifically, an infinite number of edges and vertices. The term "apeirogon" refers to a polygon with an infinite number of sides, and the term "hosohedron" refers to a polyhedron that is constructed by extending the concept of polygonal faces into three dimensions.

The term "atoroidal" generally refers to a shape or object that is not toroidal or donut-shaped. In a toroidal structure, there is a central void around which the material is distributed in a circular manner, resembling a donut. By contrast, an "atoroidal" shape would lack this characteristic of having a central void or hole, meaning it could refer to various forms such as spherical, cylindrical, or other geometrical shapes that do not incorporate the toroidal geometry.

The Baily–Borel compactification is a method used in the field of algebraic geometry and arithmetic geometry to compactify certain types of locally symmetric spaces, particularly those associated with Hermitian symmetric domains. It is named after the mathematicians William Baily and Armand Borel, who introduced the concept. ### Context and Motivation In many situations, particularly in number theory and the theory of modular forms, one deals with spaces that are not compact.

A Beltrami vector field is a type of vector field that satisfies a specific mathematical condition related to the curl operator.

The Bernoulli Quadrisection Problem refers to a geometric problem posed by Jacob Bernoulli in the late 17th century. The problem specifically asks whether it is possible to divide a given area into four equal parts using only a straightedge and a compass. The problem is more formally defined for certain types of regions, particularly looking at whether a specific area can be subdivided into four regions that are each equal in area to the entire area divided by four.

The Berry-Robbins problem is a classic problem in the field of probability theory and combinatorial optimization, particularly in the study of random processes and decision making under uncertainty. It involves a scenario where a player must decide whether to continue drawing from a box containing an unknown number of balls of a certain color or to stop and claim a reward.

The Bevan Point is a concept in the field of economics and public policy, particularly in relation to healthcare. It is named after Aneurin Bevan, the British politician who was the Minister of Health and a key architect of the National Health Service (NHS) in the UK. The term typically refers to the principles or ideals associated with Bevan's vision for a fair and equitable healthcare system.

Biangular coordinates are a type of coordinate system used primarily in two-dimensional geometry. In this system, each point in the plane is represented by a pair of angles, rather than traditional Cartesian coordinates (x, y) or polar coordinates (r, θ). Specifically, a point is defined by two angles, (α, β), which are measured from two fixed lines or reference directions.

A **blind polytope** is a concept from combinatorial geometry, particularly related to the study of polytopes and their properties. In this context, a **polytope** is a geometric object with flat sides, which can be defined in any number of dimensions. The term "blind polytope" typically refers to a specific class of polytopes that share certain combinatorial properties, particularly in relation to visibility and edges.

Bonnesen's inequality is a result in geometry that relates to the area of a convex body and the distances between points in that body. More specifically, it often pertains to the geometry of convex bodies in Euclidean spaces, particularly those shapes that can be compared based on their geometric properties. One of the well-known forms of Bonnesen's inequality deals with convex sets and relates the volume (or area) and the diameter of convex bodies.

The Butterfly curve is a well-known example of a transcendental curve in mathematics, characterized by its intricate, butterfly-like shape. It is defined using a set of parametric equations in the Cartesian coordinate system.

Cabri Geometry is a dynamic geometry software program designed for the interactive exploration and construction of geometric figures. Developed by Michel Beauduin and his team at the French company Cabri, it is widely used in education to facilitate learning and teaching of geometry concepts. Key features of Cabri Geometry include: 1. **Dynamic Construction**: Users can create geometric shapes and figures by placing points, lines, circles, and other geometric objects.

Chair tiling, also known as chair graph tiling, is a type of mathematical tiling problem that involves covering a region using shapes that are analogous to a chair. Specifically, it typically refers to using small polygons to fill a larger polygonal area without overlaps or gaps, adhering to certain constraints based on the shapes.

In various fields such as mathematics, computer science, and data analysis, the term "coarse function" can refer to a function that simplifies or abstracts details in order to provide a broader perspective or understanding of a system. 1. **Mathematics**: In the context of topology or measure theory, a coarse function might refer to an approximation or transformation that captures essential features of a space while ignoring finer details.