The Wythoff symbol is a notation used in the field of polyhedra and tilings, particularly in the context of regular and semi-regular polychora (four-dimensional analogs of polyhedra). It provides a way to describe the symmetry and structure of these geometric shapes. The notation typically consists of two numbers separated by a vertical bar, and sometimes additional information is included. The two numbers represent the arrangement of vertex angles or the types of faces around a vertex.

"Article proofs" typically refer to a stage in the academic publishing process where authors are provided with a formatted version of their manuscript, which is often referred to as a proof or galley proof. This version includes all the editorial revisions made after the original manuscript submission and allows authors to review the final layout, check for any typographical errors, and ensure that their work is accurately represented before the article is published in a journal.

Ovi, or "Ovi poetry," refers to a traditional form of poetry from the Indian subcontinent, specifically associated with the folk traditions of the state of Maharashtra and other regions. It is characterized by its simple language, rhythmic structure, and often conveys themes related to daily life, nature, love, and the struggles of the common people. Ovi poems are typically sung or recited, often during festivals or communal gatherings, and they hold significant cultural value in preserving oral traditions.

Mathematics educators are professionals who specialize in teaching and facilitating the learning of mathematics. They can work at various educational levels, including elementary, middle, and high schools, as well as in colleges and universities. Their primary goal is to help students understand mathematical concepts, develop problem-solving skills, and encourage a positive attitude toward mathematics. Key roles of mathematics educators include: 1. **Curriculum Development**: Designing math curricula and instructional materials that are engaging and effective in teaching mathematical concepts.

Mathematics education awards are recognitions given to individuals, organizations, or programs that have made significant contributions to the field of mathematics education. These awards can honor teachers, researchers, writers, and institutions that have demonstrated excellence in teaching, curriculum development, educational research, or advocacy for the importance of mathematics education. Some common types of mathematics education awards include: 1. **Teaching Awards**: Recognizing outstanding mathematics educators at various levels, from elementary to higher education.

Professorships in mathematics refer to academic positions held by scholars who are responsible for teaching, conducting research, and contributing to the academic community within the field of mathematics. These positions can vary in rank, including titles such as Assistant Professor, Associate Professor, and Full Professor, each reflecting different levels of experience, achievement, and responsibility.

A basic dimension typically refers to a fundamental measurement or parameter used to describe the properties of an object or physical phenomenon. In various fields, "basic dimension" can have slightly different meanings: 1. **Mathematics/Geometry**: Basic dimensions often refer to the fundamental aspects of geometric shapes, such as length, width, height, area, and volume. These dimensions help characterize the size and shape of objects.