Lecture

Faces, Facets and Vertices

Related lectures (30)

Covers the 2D case of polynomial encroaching and vertices of polyhedra.

Explores the definitions and symmetries of regular polyhedra, shedding light on ancient geometry and modern mathematical formalization.

Explores the definitions and symmetries of regular polyhedra, focusing on the five known convex regular polyhedra from ancient times.

Explores extreme points, vertices, and basic feasible solutions in polyhedra, emphasizing their properties and construction.

Explores the properties of regular polyhedra, their symmetries, generation, and historical misconceptions.

Explores convex polyhedra, linear programs, and their optimization importance.

Explores the composition of applications in mathematics and the importance of understanding their properties.

Demonstrates the process of including beams and correcting orientations for complex configurations.

Covers proper and cast shadows in descriptive geometry with practical examples and exercises.

Explores the historical background and significance of symmetries in regular polyhedra, shedding new light on Euclid's Elements.

Explores separating hyperplanes for two sets X and Y, discussing conditions for separation and implications of convexity.

Explores harmonic ratio in geometry, covering bisectors, harmonic segments, polyhedra, spatial curves, and historical perspectives.

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Covers the concept of integer cones and Carathéodory's theorem with illustrative examples.

Explores polygons, polyhedra, regularity, and starred configurations in Euclidean geometry, highlighting historical context and limitations.

Focuses on proving the Cellular Approximation Theorem, introducing polyhedra and piecewise linear maps.

Explores symmetry in modern geometry, emphasizing reflections, rotations, and practical applications in computer-aided design.

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.