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 harmonic quadrilateral is a specific type of quadrilateral in the realm of projective geometry, characterized by a particular relationship between its vertices. A quadrilateral is considered harmonic if the pairs of opposite sides are divided proportionally by the intersection of the diagonals.

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

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.

A **complex Lie group** is a mathematical structure that combines the concepts of Lie groups and complex analysis. Specifically, a complex Lie group is a group that is both a smooth manifold and a complex manifold, equipped with a group operation that is compatible with both the manifold structures. Here are some key points to understand complex Lie groups: 1. **Lie Groups**: A Lie group is a group that is also a differentiable manifold, meaning it has a layer of smoothness (i.e.

The Murakami–Yano formula is a result in differential geometry, specifically concerning the relationship between the curvature of a Riemannian manifold and the behavior of the volume of the manifold under certain geometric transformations. Named after mathematicians Hideo Murakami and Yoshihiro Yano, the formula provides a way to compute the derivative of the volume of a Riemannian manifold when the metric is varied.

Exotic affine space typically refers to certain mathematical constructions in the realm of differential geometry, algebraic geometry, and topology. However, the specific term "exotic affine space" isn't standard in mathematical literature, so it may be context-dependent. 1. **Affine Space**: An affine space is a set of points equipped with a vector space that associates vectors between points.

Kosnita's theorem is a result in the field of geometry, specifically in relation to cyclic polygons and triangle centers.

Laplacian smoothing, also known as Laplacian regularization or Laplacian filtering, is a technique used in various fields, including computer graphics, machine learning, and signal processing, to improve the quality of data representation or to enhance smoothness in a given dataset.

The Mukhopadhyaya Theorem is a result in the field of number theory, specifically concerning the properties of Diophantine equations. However, it's important to note that it may not be widely known or recognized in all mathematical circles, and the presentation of the theorem may vary. In general, the theorem deals with the conditions under which certain types of integer solutions exist for equations of specific forms. It may also relate to topics in algebraic number theory or algebraic geometry.

Order-2 apeirogonal tiling refers to a specific type of tiling pattern in the study of geometry, particularly in the context of regular tiling in the Euclidean plane or in hyperbolic spaces. The term "apeirogon" refers to a polygon with an infinite number of sides, which is a theoretical construct.

The Padovan cuboid spiral is a geometric figure that extends the concept of the Padovan sequence into three dimensions. The Padovan sequence is defined by the recurrence relation \( P(n) = P(n-2) + P(n-3) \) with initial values \( P(0) = 1 \), \( P(1) = 1 \), and \( P(2) = 1 \). Subsequent values can be derived from these.

A quaternionic polytope is a generalization of the concept of a polytope in the context of quaternionic geometry, much like how a polytope can be generalized from Euclidean spaces to spaces based on complex numbers. In basic terms, a polytope in Euclidean space is defined as a geometric object with flat sides, which can exist in any number of dimensions. A typical example is a polygon in 2D or a polyhedron in 3D.

Seiffert's spiral is a mathematical curve that is defined as the locus of points that satisfy a particular relationship between parametric equations. It is similar in concept to other spirals, such as the Archimedean spiral and the logarithmic spiral, but it has its own unique properties.

As of my last update in October 2023, "Superegg" may refer to different things depending on the context. It could potentially relate to various sectors such as technology, gaming, education, or product branding. For example, in the tech industry, it might be a name for a startup, app, or innovative product. In gaming, it might represent a specific game, character, or feature.

The small stellated 120-cell, also known as the stellated 120-cell or the small stellated hyperdiamond, is a specific type of honeycomb in four-dimensional space, classified among the convex regular 4-polytopes. It is a part of the family of 4-dimensional polytopes known as honeycombs, which are tessellations of four-dimensional space.

A toric section refers to a curve obtained by intersecting a torus (the surface shaped like a doughnut) with a plane. The intersection can produce different types of curves depending on how the plane intersects the torus. The possible outcomes include: 1. **Circle**: If the plane intersects the torus parallel to its axis of rotation. 2. **Ellipse**: If the plane intersects the torus at an angle but does not pass through the central hole of the torus.

As of my last knowledge update in October 2021, there is no widely recognized information regarding an individual or entity named "Derek Keir." It’s possible that this name might refer to a private individual, a less-known public figure, or a fictional character. It could also be a name that gained prominence after my last update.

Lisa Tauxe is a prominent American geophysicist known for her research in the fields of paleomagnetism and geomagnetism. She is recognized for her work on the Earth's magnetic field and its changes over geological time, as well as for her contributions to understanding the relationship between the magnetic field and plate tectonics. Tauxe has published numerous scientific papers and has been involved in educational outreach in geosciences. She has also served in various leadership roles within scientific communities.