In mathematics, a Catalan solid, or Archimedean dual, is a dual polyhedron to an Archimedean solid. There are 13 Catalan solids. They are named for the Belgian mathematician, Eugène Catalan, who first described them in 1865. The Catalan solids are all convex. They are face-transitive but not vertex-transitive. This is because the dual Archimedean solids are vertex-transitive and not face-transitive. Note that unlike Platonic solids and Archimedean solids, the faces of Catalan solids are not regular polygons. However, the vertex figures of Catalan solids are regular, and they have constant dihedral angles. Being face-transitive, Catalan solids are isohedra. Additionally, two of the Catalan solids are edge-transitive: the rhombic dodecahedron and the rhombic triacontahedron. These are the duals of the two quasi-regular Archimedean solids. Just as prisms and antiprisms are generally not considered Archimedean solids, so bipyramids and trapezohedra are generally not considered Catalan solids, despite being face-transitive. Two of the Catalan solids are chiral: the pentagonal icositetrahedron and the pentagonal hexecontahedron, dual to the chiral snub cube and snub dodecahedron. These each come in two enantiomorphs. Not counting the enantiomorphs, bipyramids, and trapezohedra, there are a total of 13 Catalan solids. (Wikipedia).
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From playlist Measuring Basic Shapes
What's the difference between concrete and cement? Concrete is the most important construction material on earth and foundation of our modern society. At first glance it seems rudimentary, but there is a tremendous amount of complexity involved in every part of designing and placing conc
From playlist Civil Engineering
Delta-Star is a polyhedral object which I invented in 1996. The type of Delta-Star corresponds to Deltahedrons. It expands and shrinks.
From playlist Handmade geometric toys
Dihedral Group (Abstract Algebra)
The Dihedral Group is a classic finite group from abstract algebra. It is a non abelian groups (non commutative), and it is the group of symmetries of a regular polygon. This group is easy to work with computationally, and provides a great example of one connection between groups and geo
From playlist Abstract Algebra
Catalan's Constant and the Taylor Series of the Inverse Tangent! [ + Exploring Python and Desmos ]
Help me create more free content! =) https://www.patreon.com/mathable Merch :v - https://teespring.com/de/stores/papaflammy https://shop.spreadshirt.de/papaflammy 2nd Channel: https://www.youtube.com/channel/UCPctvztDTC3qYa2amc8eTrg Let us dive into some analytic numbe
From playlist Taylor Series
Trapeze Bear Wooden Toy 3D Model
An old toy, very common in the past. Usually made of wood, but also with plastic. Again, the problem is the strings. So I used a few tricks to simulate it. Far from perfect, just to have some fun. Modeled with Solidworks 2015. Rendered with Simlab Composer 6 Mechanical Edition. Free 3D mod
From playlist Wooden Toys
Physics - Mechanics: Torsion (11 of 14) Torsion and a Hollow Tube
Visit http://ilectureonline.com for more math and science lectures! In this video I will derive the equation of torque=? of the torsion of a hollow tube. Next video in this series can be found at: https://youtu.be/mQ-wseAfAlc
From playlist PHYSICS 16.6 TORSION
Modified Logarithmic Sobolev Inequalities: Theory, (lecture 2) by Prasad Tetali
PROGRAM: ADVANCES IN APPLIED PROBABILITY ORGANIZERS: Vivek Borkar, Sandeep Juneja, Kavita Ramanan, Devavrat Shah, and Piyush Srivastava DATE & TIME: 05 August 2019 to 17 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Applied probability has seen a revolutionary growth in resear
From playlist Advances in Applied Probability 2019
Marjorie Wikler Senechal - Unwrapping a Gem - CoM Apr 2021
If the celebrated Scottish zoologist D’Arcy W. Thompson (1860 – 1948) could have met the near-legendary German astronomer Johannes Kepler (1571 – 1630), what would they talk about? Snowflakes, maybe? It is true that both men wrote about their hexagonal shapes. But they both wrote about Arc
From playlist Celebration of Mind 2021
Adam Savage's One Day Builds: Rhombic Dodecahedron with Matt Parker!
Buy Matt Parker's Humble Pi: https://amzn.to/367UmBV In this special One Day Build filmed earlier this year, mathematician Matt Parker visits the cave to build a rhombic dodecahedron with Adam! Be prepared for lots of fun geometry discussion as Adam and Matt try to make abstract math conc
From playlist Adam Savage's One Day Builds
Catalonia independence referendum
Support CaspianReport through Patreon: https://www.patreon.com/CaspianReport BAKU - Tensions are high between Catalan and Spanish authorities over the former’s referendum on independence, which is scheduled for October 1st, 2017. As Catalan resident prepare to vote on whether they want to
From playlist Geopolitics
Live Coding: Bending Light - Part 2
In this video we'll build on the beginning we made last time and will make a gem stone and add special effects like chromatic aberration and out scattering. ========== Social Media Links ========== Twitter: @The_ArtOfCode Facebook: https://www.facebook.com/groups/theartofcode/ Patreon:
From playlist Shader Coding
2 Construction of a Matrix-YouTube sharing.mov
This video shows you how a matrix is constructed from a set of linear equations. It helps you understand where the various elements in a matrix comes from.
From playlist Linear Algebra
Andrew Sutherland: Moment sequences of Sato-Tate groups
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Jean-Morlet Chair - Shparlinski/Kohel
Andrew Sutherland: Introduction to Sato-Tate distributions
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Jean-Morlet Chair - Shparlinski/Kohel
15-year-old did mathematical research?! What was my thinking process back then?
Mathematical research can be accessible. This video series somewhat faithfully records the thinking process of a 15-year-old in his mathematical research. Although it turned out that someone had made a similar discovery, this independent and nontrivial discovery still stands to prove that
From playlist Miscellaneous
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
Delta-Star is a polyhedral object which I invented in 1996. The type of Delta-Star corresponds to Deltahedrons. It expands and shrinks. Especially highly symmetric tetrahedron,octahedron,icosahedron types and hexahedron,decahedron types can transform smoothly.
From playlist Handmade geometric toys