# 9-orthoplex

In geometry, a 9-orthoplex or 9-cross polytope, is a regular 9-polytope with 18 vertices, 144 edges, 672 triangle faces, 2016 tetrahedron cells, 4032 5-cells 4-faces, 5376 5-simplex 5-faces, 4608 6-simplex 6-faces, 2304 7-simplex 7-faces, and 512 8-simplex 8-faces. It has two constructed forms, the first being regular with Schläfli symbol {37,4}, and the second with alternately labeled (checkerboarded) facets, with Schläfli symbol {36,31,1} or Coxeter symbol 611. It is one of an infinite family of polytopes, called cross-polytopes or orthoplexes. The dual polytope is the 9-hypercube or enneract. (Wikipedia).

Orthocenters exist! | Universal Hyperbolic Geometry 10 | NJ Wildberger

In classical hyperbolic geometry, orthocenters of triangles do not in general exist. Here in universal hyperbolic geometry, they do. This is a crucial building block for triangle geometry in this subject. The dual of an orthocenter is called an ortholine---also not seen in classical hyperb

From playlist Universal Hyperbolic Geometry

Orthogonality and Orthonormality

We know that the word orthogonal is kind of like the word perpendicular. It implies that two vectors have an angle of ninety degrees or half pi radians between them. But this term means much more than this, as we can have orthogonal matrices, or entire subspaces that are orthogonal to one

From playlist Mathematics (All Of It)

Seminar on Applied Geometry and Algebra (SIAM SAGA): Dustin Mixon

Title: Packing Points in Projective Spaces Speaker: Dustin Mixon Date: Tuesday, March 8, 2022 at 11:00am Eastern Abstract: Given a compact metric space, it is natural to ask how to arrange a given number of points so that the minimum distance is maximized. For example, the setting of the

From playlist Seminar on Applied Geometry and Algebra (SIAM SAGA)

What are four types of polygons

👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1

From playlist Classify Polygons

X4 ORTHOCENTER

The orthocenter (X4) is the meet of the altitudes of a triangle. It's not obvious that these meet! ************************ Here are the Wild Egg Maths Playlists (some available only to Members!) Algebraic Calculus One (for the Open Learning Course) : https://www.youtube.com/playlist?lis

From playlist Triangle Geometry

Orthogonal and Orthonormal Sets of Vectors

This video defines orthogonal and orthonormal sets of vectors.

From playlist Orthogonal and Orthonormal Sets of Vectors

9mat Co-ordinates

getting started

From playlist 2014 9mat

Group theory 9: Quaternions

This is lecture 9 of an online mathematics course on groups theory. It covers the quaternions group and its realtion to the ring of quaternions.

From playlist Group theory

What is an obtuse triangle

👉 Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl

From playlist Types of Triangles and Their Properties

What is the difference between convex and concave

👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1

From playlist Classify Polygons

This Problem Stumped Vietnamese Students - Solution To Viral Puzzler

This problem was asked to students in Vietnam. Can you figure it out? Place the numbers 1 to 9, using each number once, to make a valid equation. In this video I explain how you can solve this problem logically. UPDATE: I've posted all 136 solutions, at the end of this description, found

From playlist Viral Math Memes

Between 1&9 Sudoku AKA "Sandwich Sudoku"!

Simon takes a look at this outstanding puzzle created by one of our viewers, thank you Isaac Resnikoff. We're also delighted to note that Alex Bellos, author of some brilliant puzzle books (like Alex's Adventures In Numberland), has written an article about our channel and this Sudoku var

From playlist "Sandwich Sudoku"/Between 1&9 Sudoku

Decomposing a fraction visually | Fractions | Pre-Algebra | Khan Academy

It helps to visually understand what decomposing a fraction looks like. We're pretty sure you're going to like this. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/decomposing-fractions-pre-alg/e/decomposing-fract

From playlist Fractions | Pre-Algebra | Khan Academy

Does 0.9999… = 1?

This video shows three reasons why 0.9999… equals 1.

From playlist Mathematics General Interest

EngageNY Grade 3 Module 3 Lesson 13

EngageNY/Eureka Math Grade 3 Module 3 Lesson 13 For more videos, please visit http://bit.ly/engageportal

From playlist EngageNY Grade 3 Module 3

Sum & Product of Cosines (3 of 3: Drawing ℝ conclusions)

More resources available at www.misterwootube.com

From playlist Using Complex Numbers

Write and Determine a Difference Describing an Situation

This video explains how to write and determine a difference to solve an application. The difference is determined on the number line and formally. http://mathispower4u.com

From playlist Adding and Subtracting Integers

What is an isosceles triangle

👉 Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl

From playlist Types of Triangles and Their Properties

A sudoku with only 3 givens? How is that even possible?

An elegant variant sudoku from the UK Open Sudoku tournament. This is called "Between 1 & 9" sudoku

From playlist "Sandwich Sudoku"/Between 1&9 Sudoku