Polyhedral stellation | Polyhedra

Final stellation of the icosahedron

In geometry, the complete or final stellation of the icosahedron is the outermost stellation of the icosahedron, and is "complete" and "final" because it includes all of the cells in the icosahedron's stellation diagram. That is, every three intersecting face planes of the icosahedral core intersect either on a vertex of this polyhedron, or inside of it. This polyhedron is the seventeenth stellation of the icosahedron, and given as Wenninger model index 42. As a geometrical figure, it has two interpretations, described below: * As an irregular with 20 identical self-intersecting enneagrammic faces, 90 edges, 60 vertices. * As a with 180 triangular faces (60 isosceles, 120 scalene), 270 edges, and 92 vertices. This interpretation is useful for polyhedron model building. Johannes Kepler researched stellations that create regular star polyhedra (the Kepler-Poinsot polyhedra) in 1619, but the complete icosahedron, with irregular faces, was first studied in 1900 by Max Brückner. (Wikipedia).

Final stellation of the icosahedron
Video thumbnail

Fractal Snowflakes, Symmetries, and Beautiful Math Decorations

Keep exploring at ► https://brilliant.org/TreforBazett. Get started for free, and hurry—the first 200 people get 20% off an annual premium subscription. Today is MATH CRAFTS day! We're going to make some holiday decorations and then also chat about the cool math behind them. We'll learn a

From playlist Cool Math Series

Video thumbnail

Michael Tanoff - Son of O'Gara - G4G12 April 2016

Mathematical philately over the past half century

From playlist G4G12 Videos

Video thumbnail

Live CEOing Ep 186: Polyhedra in Wolfram Language

Watch Stephen Wolfram and teams of developers in a live, working, language design meeting. This episode is about Polyhedra in the Wolfram Language.

From playlist Behind the Scenes in Real-Life Software Design

Video thumbnail

Magnet Satisfaction Extreme | Magnetic Games

I think this is my most satisfying video ever, what do you think? A bit of magnetic sculptures, lights and diamagnetic levitation. And the sounds? I love the sound of pyrolytic graphite falling on magnets, I hope also like lovers of ASMR. Here the magnets used to build those magnetic scul

From playlist WAVES

Video thumbnail

Robert Fathauer - Tessellations: Mathematics, Art, and Recreation - CoM Apr 2021

A tessellation, also known as a tiling, is a collection of shapes (tiles) that fit together without gaps or overlaps. Tessellations are a topic of mathematics research as well as having many practical applications, the most obvious being the tiling of floors and other surfaces. There are n

From playlist Celebration of Mind 2021

Video thumbnail

Solving a quadratic by completing the square | Part 1

👉 Learn how to solve quadratic equations by completing the square. When solving a quadratic equation by completing the square, we first take the constant term to the other side of the equation and create a perfect square trinomial with the quadratic term and the linear term. This is done

From playlist Solve a Quadratic by Completing the Square | x^2+bx+c

Video thumbnail

Solving an equation by completing the square

👉 Learn how to solve quadratic equations by completing the square. When solving a quadratic equation by completing the square, we first take the constant term to the other side of the equation and create a perfect square trinomial with the quadratic term and the linear term in the right ha

From playlist Solve a Quadratic by Completing the Square | Fractions

Video thumbnail

Interactivity: Building and App in 60 Seconds

With the Wolfram Language and Mathematica, you really can build a useful, interactive app for exploring ideas in just 60 seconds. Starting with the 60-second app, this talk covers the ins and outs of the Wolfram Language function Manipulate, the key to instantly interactive interfaces. You

From playlist Geek Out with Wolfram Virtual Workshop 2014

Video thumbnail

Solving a quadratic by completing the square

👉 Learn how to solve quadratic equations by completing the square. When solving a quadratic equation by completing the square, we first take the constant term to the other side of the equation and create a perfect square trinomial with the quadratic term and the linear term in the right ha

From playlist Solve a Quadratic by Completing the Square | Fractions

Video thumbnail

Solving a quadratic by completing the square

👉 Learn how to solve quadratic equations by completing the square. When solving a quadratic equation by completing the square, we first take the constant term to the other side of the equation and create a perfect square trinomial with the quadratic term and the linear term in the right ha

From playlist Solve a Quadratic by Completing the Square | Fractions

Video thumbnail

Solving a quadratic by completing the square

👉 Learn how to solve quadratic equations by completing the square. When solving a quadratic equation by completing the square, we first take the constant term to the other side of the equation and create a perfect square trinomial with the quadratic term and the linear term in the right ha

From playlist Solve a Quadratic by Completing the Square | Fractions

Video thumbnail

My #MegaFavNumbers 19,958,400 and stellated polygons

from what I have found online, stellations don't seem to be all that well known, so I hope this video will help it become a more commonly talked about concept, because I found it very interesting, especially after I had to do the proof myself, I got a lot of good insights out of it.

From playlist MegaFavNumbers

Video thumbnail

Solving a quadratic by completing the square

👉 Learn how to solve quadratic equations by completing the square. When solving a quadratic equation by completing the square, we first take the constant term to the other side of the equation and create a perfect square trinomial with the quadratic term and the linear term. Timestamps: 0

From playlist Solve a Quadratic by Completing the Square | x^2+bx+c

Video thumbnail

Solving an equation by completing the square

👉 Learn how to solve quadratic equations by completing the square. When solving a quadratic equation by completing the square, we first take the constant term to the other side of the equation and create a perfect square trinomial with the quadratic term and the linear term. This is done

From playlist Solve a Quadratic by Completing the Square | x^2+bx+c

Video thumbnail

Solving an equation by completing the square

👉 Learn how to solve quadratic equations by completing the square. When solving a quadratic equation by completing the square, we first take the constant term to the other side of the equation and create a perfect square trinomial with the quadratic term and the linear term. This is done

From playlist Solve a Quadratic by Completing the Square | x^2+bx+c

Video thumbnail

Solving by completing the square

👉 Learn how to solve quadratic equations by completing the square. When solving a quadratic equation by completing the square, we first take the constant term to the other side of the equation and create a perfect square trinomial with the quadratic term and the linear term in the right ha

From playlist Solve a Quadratic by Completing the Square | Fractions

Video thumbnail

Laura Taalman - 3D printed Hinged Dissections and Foldable Polyhedra - CoM Apr 2021

We’ll talk briefly about 3D printing foldable and hinged models for polygonal and polyhedral dissections, and a new idea for “volume nets” for which I am seeking feedback. Included will be access to 3D design files that people can use to create their own models. Q&A at the end can extend t

From playlist Celebration of Mind 2021

Video thumbnail

Step by step process explaining completing the square to solve

👉 Learn how to solve quadratic equations by completing the square. When solving a quadratic equation by completing the square, we first take the constant term to the other side of the equation and create a perfect square trinomial with the quadratic term and the linear term. This is done

From playlist Solve a Quadratic by Completing the Square | x^2+bx+c

Related pages

Icosahedral symmetry | Convex hull | Harmonices Mundi | List of Wenninger polyhedron models | Orthographic projection | Star polyhedron | Enneagram (geometry) | Small stellated dodecahedron | Regular polyhedron | J. C. P. Miller | Augustin-Louis Cauchy | Dodecahedron | Euler characteristic | Great icosahedron | Harold Scott MacDonald Coxeter | Isogonal figure | Golden ratio | Star polygon | Icosahedron | Great stellated dodecahedron | Symmetry group | Max Brückner | Truncated icosahedron | Polyhedron | Stellation | Polyhedron model | Patrick du Val | Great dodecahedron | Regular Polytopes (book) | Stellation diagram | Kepler–Poinsot polyhedron | Geometry | Noble polyhedron