# Tetrahedron

In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the ordinary convex polyhedra and the only one that has fewer than 5 faces. The tetrahedron is the three-dimensional case of the more general concept of a Euclidean simplex, and may thus also be called a 3-simplex. The tetrahedron is one kind of pyramid, which is a polyhedron with a flat polygon base and triangular faces connecting the base to a common point. In the case of a tetrahedron the base is a triangle (any of the four faces can be considered the base), so a tetrahedron is also known as a "triangular pyramid". Like all convex polyhedra, a tetrahedron can be folded from a single sheet of paper. It has two such nets. For any tetrahedron there exists a sphere (called the circumsphere) on which all four vertices lie, and another sphere (the insphere) tangent to the tetrahedron's faces. (Wikipedia).

How to construct a Tetrahedron

How the greeks constructed the first platonic solid: the regular tetrahedron. Source: Euclids Elements Book 13, Proposition 13. In geometry, a tetrahedron also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. Th

From playlist Platonic Solids

Regular polyhedra

This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/q0PF.

From playlist 3D printing

Cardboard Tetrahedron Pyramid Perfect Circle Solar How to make a pyramid out of cardboard

How to make a pyramid out of cardboard. A tetrahedron is a polyhedron composed of four triangular faces, three of which meet at each vertex.

From playlist HOME OF GREENPOWERSCIENCE SOLAR DIY PROJECTS

Unique way to divide a tetrahedron in half

This is an interesting geometry volume problem using tetrahedrons. We use the volume of a tetrahedron and Cavalieri's principle in 3D.

From playlist Platonic Solids

The geometry of the regular tetrahedron | Universal Hyperbolic Geometry 45 | NJ Wildberger

We look at the geometry of the regular tetrahedron, from the point of view of rational trigonometry. In particular we re-evaluate an important angle for chemists formed by the bonds in a methane molecule, and obtain an interesting rational spread instead. Video Content: 00:00 Introduction

From playlist Universal Hyperbolic Geometry

Complete Explanation for Volume of a Tetrahedron

In this video we derive the volume of a tetrahedron with the help of Euclid.

From playlist Platonic Solids

Can you prove this 2000 year old textbook problem?

Proving the tetrahedron consists of 4 equilateral triangles. This has been submitted into the 3blue1brown video competition. https://www.etsy.com/listing/1037552189/wooden-large-platonic-solids-geometry https://www.amazon.com/dp/B093D22DGN https://books.apple.com/us/book/euclids-elements-

From playlist Platonic Solids

2003 AIME II problem 4 (part 1) | Math for fun and glory | Khan Academy

Created by Sal Khan. Watch the next lesson: https://www.khanacademy.org/math/math-for-fun-and-glory/aime/2003-aime/v/2003-aime-ii-problem-4-part-2?utm_source=YT&utm_medium=Desc&utm_campaign=mathforfunandglory Missed the previous lesson? https://www.khanacademy.org/math/math-for-fun-and-g

From playlist AIME | Math for fun and glory | Khan Academy

Three dimensional geometry, Zome, and the elusive tetrahedron (Pure Maths Seminar, Aug 2012)

This is a Pure Maths Seminar given in Aug 2012 by Assoc Prof N J Wildberger of the School of Mathematics and Statistics UNSW. The seminar describes the trigonometry of a tetrahedron using rational trigonometry. Examples are taken from the Zome construction system.

From playlist Pure seminars

Average height | MIT 18.02SC Multivariable Calculus, Fall 2010

Average height Instructor: Joel Lewis View the complete course: http://ocw.mit.edu/18-02SCF10 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

The Tetrahedral Boat - Numberphile

Featuring Marcus du Sautoy discussing polyhedra and the art of Conrad Shawcross... More links & stuff in full description below ↓↓↓ Marcus du Sautoy website: https://www.simonyi.ox.ac.uk Marcus' books on Amazon: https://amzn.to/33YbOxS More videos with Marcus: https://bit.ly/Marcus_Number

From playlist Marcus Du Sautoy on Numberphile

Stanford artist collaborates with physics department for 'Drawing with Tetrahedra'

Physics faculty members and graduate students use tetrahedra to create a less-than-perfect structure that explores the connection between shape and sound. For more information, see: http://news.stanford.edu/news/2014/march/tetra-physics-vivaldi-040214.html

From playlist Stanford Highlights

Regular triangulation of H³

This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/nicy. Tiling of H^2 image from http://en.wikipedia.org/wiki/File:H2checkers_iii.png

From playlist 3D printing

Tetrahedron decomposition (pure CSS 3D)

You can see the live demo here https://codepen.io/thebabydino/pen/OjgWQG/ If the work I've been putting out since early 2012 has helped you in any way or you just like it, please consider supporting it to help me continue and stay afloat. You can do so in one of the following ways: * yo

From playlist CSS variables

Triple integrals to find volume of the solid (KristaKingMath)

► My Multiple Integrals course: https://www.kristakingmath.com/multiple-integrals-course Learn how to use triple integrals to find the volume of a solid. In this case, we'll find the volume of the tetrahedron enclosed by the three coordinate planes and another function. We'll need to find

From playlist Calculus III

Do tetrahedrons tessellate space? #Shorts

Tessellate is when you fit together closely shapes without gaps or overlapping. Squares can tessellate a plane. Cubes can tessellate a space. Regular Triangles can tessellate a plane. Do regular tetrahedrons tessellate space?

From playlist #shorts mathematicsonline

Joel Hass - Lecture 3 - Algorithms and complexity in the theory of knots and manifolds - 20/06/18

School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects (http://geomschool2018.univ-mlv.fr/) Joel Hass (University of California at Davis, USA) Algorithms and complexity in the theory of knots and manifolds Abstract: These lectures will introduce algorithmic pro