4-polytopes | Four-dimensional geometry | Algebraic topology

4-polytope

In geometry, a 4-polytope (sometimes also called a polychoron, polycell, or polyhedroid) is a four-dimensional polytope. It is a connected and closed figure, composed of lower-dimensional polytopal elements: vertices, edges, faces (polygons), and cells (polyhedra). Each face is shared by exactly two cells. The 4-polytopes were discovered by the Swiss mathematician Ludwig Schläfli before 1853. The two-dimensional analogue of a 4-polytope is a polygon, and the three-dimensional analogue is a polyhedron. Topologically 4-polytopes are closely related to the uniform honeycombs, such as the cubic honeycomb, which tessellate 3-space; similarly the 3D cube is related to the infinite 2D square tiling. Convex 4-polytopes can be cut and unfolded as nets in 3-space. (Wikipedia).

4-polytope
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Using a set of points determine if the figure is a parallelogram using the midpoint formula

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From playlist Quadrilaterals on a Coordinate Plane

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What is the 4th Dimension REALLY? - 4D Golf Devlog #2

A more practical explanation for those interested in exploring 4D spaces. For those not already familiar with basic 4D concepts, here's some videos I can recommend: "Visualizing 4D Geometry" https://www.youtube.com/watch?v=4URVJ3D8e8k "The things you'll find in higher dimensions" https:/

From playlist 4D Golf

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What are four types of polygons

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From playlist Classify Polygons

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Determining if a set of points is a rhombus, square or rectangle

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From playlist Quadrilaterals on a Coordinate Plane

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Determine if a set of points is a parallelogram using the distance formula

👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr

From playlist Quadrilaterals on a Coordinate Plane

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Determining if a set of points makes a parallelogram or not

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From playlist Quadrilaterals on a Coordinate Plane

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From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels

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Using the slope formula to determine if points make up a rectangle

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From playlist Kavli Asian Winter School (KAWS) on Strings, Particles and Cosmology 2018

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From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra

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Volker Kaibel: A simple geometric proof showing that almost all 01 polytopes have exponential ...

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From playlist HIM Lectures: Trimester Program "Combinatorial Optimization"

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Tropical Geometry - Lecture 12 - Geometric Tropicalization | Bernd Sturmfels

Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)

From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels

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Spectrahedral lifts of convex sets – Rekha Thomas – ICM2018

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Tropical Geometry - Lecture 9 - Tropical Convexity | Bernd Sturmfels

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From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels

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Determine if a set of points is a trapezoid or not

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From Gentle algebras to S-matrix in Quantum Field Theory by Alok Laddha

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Karim Alexander Adiprasito: New Construction for projectively unique polytopes

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From playlist HIM Lectures: Trimester Program "Universality and Homogeneity"

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Introduction to geometric invariant theory 2: Moment polytopes - Michael Walter

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From playlist Mathematics

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Determine if a set of points is a parallelogram by using the slope formula

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From playlist Quadrilaterals on a Coordinate Plane

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