In geometry, an Archimedean solid is one of the 13 solids first enumerated by Archimedes. They are the convex uniform polyhedra composed of regular polygons meeting in identical vertices, excluding the five Platonic solids (which are composed of only one type of polygon), excluding the prisms and antiprisms, and excluding the pseudorhombicuboctahedron. They are a subset of the Johnson solids, whose regular polygonal faces do not need to meet in identical vertices. "Identical vertices" means that each two vertices are symmetric to each other: A global isometry of the entire solid takes one vertex to the other while laying the solid directly on its initial position. Branko Grünbaum observed that a 14th polyhedron, the elongated square gyrobicupola (or pseudo-rhombicuboctahedron), meets a weaker definition of an Archimedean solid, in which "identical vertices" means merely that the faces surrounding each vertex are of the same types (i.e. each vertex looks the same from close up), so only a local isometry is required. Grünbaum pointed out a frequent error in which authors define Archimedean solids using this local definition but omit the 14th polyhedron. If only 13 polyhedra are to be listed, the definition must use global symmetries of the polyhedron rather than local neighborhoods. Prisms and antiprisms, whose symmetry groups are the dihedral groups, are generally not considered to be Archimedean solids, even though their faces are regular polygons and their symmetry groups act transitively on their vertices. Excluding these two infinite families, there are 13 Archimedean solids. All the Archimedean solids (but not the elongated square gyrobicupola) can be made via Wythoff constructions from the Platonic solids with tetrahedral, octahedral and icosahedral symmetry. (Wikipedia).
This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/MYI
From playlist 3D printing
Platonic and Archimedean solids
Platonic solids: http://shpws.me/qPNS Archimedean solids: http://shpws.me/qPNV
From playlist 3D printing
Archimedes' Principle in the Molecular World
How Archimedes' Principle emerges from the behavior of atoms and molecules. My Patreon page is at https://www.patreon.com/EugeneK
From playlist Physics
The green and orange wheels of Archimedean grooves are identical. The green one is input. The pink pin slides in both grooves and in a straight slot of a immobile bar. The slot is on the line connecting axes of the two wheels. Two wheels rotate in the same direction with the same speed, li
From playlist Mechanisms
Fluids, Buoyancy, and Archimedes' Principle
Archimedes is not just the owl from the Sword in the Stone. Although that's a sweet movie if you haven't seen it. He was also an old Greek dude who figured out a bunch of physics way before other people did. Some of this was discovered at bath time, so it has a lot to do with water, but do
From playlist Classical Physics
Archimedes Spiral Gear Mechanism
This unusual gear mechanism is based around an Archimedes Spiral. Tim was given it by a friend, who made it using 3D printing. Happy New Year to you all from everyone at Grand Illusions!
From playlist Engineering
The green and orange coaxial wheels of Archimedean grooves are identical. The pink pin slides in both grooves and in a straight slot of a fixed bar. The two wheels rotate in opposite directions with the same speed. Pitch of the Archimedean groove must be big enough to prevent possible jam.
From playlist Mechanisms
Device for milling Archimedean spiral groove 1
Combination of bevel gear satellite drive and nut-screw one.
From playlist Mechanisms
Physical Science 4.1d - Archimedes
Archimedes and some of his early inventions. The Archimedes Screw, the Claw of Archimedes.
From playlist Physical Science Chapter 4
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
AlgTop8: Polyhedra and Euler's formula
We investigate the five Platonic solids: tetrahedron, cube, octohedron, icosahedron and dodecahedron. Euler's formula relates the number of vertices, edges and faces. We give a proof using a triangulation argument and the flow down a sphere. This is the eighth lecture in this beginner's
From playlist Algebraic Topology: a beginner's course - N J Wildberger
Playing with Platonic and Archimedean Solids by Swati Sircar and Susy Varughese
SUMMER SCHOOL FOR WOMEN IN MATHEMATICS AND STATISTICS POPULAR TALKS (TITLE AND ABSTRACT) June 17, Friday, 15:45 - 16:45 hrs Swati Sircar (AzimPremji University, Bengaluru, India) Title: Playing with Platonic and Archimedean Solids Abstract: While the 5 Platonic solids are quite popular
From playlist Summer School for Women in Mathematics and Statistics - 2022
Thin Groups and Applications - Alex Kontorovich
Analysis and Beyond - Celebrating Jean Bourgain's Work and Impact May 21, 2016 More videos on http://video.ias.edu
From playlist Analysis and Beyond
Uniform Tilings of The Hyperbolic Plane (Lecture 4) by Subhojoy Gupta
ORGANIZERS : C. S. Aravinda and Rukmini Dey DATE & TIME: 16 June 2018 to 25 June 2018 VENUE : Madhava Lecture Hall, ICTS, Bangalore This workshop on geometry and topology for lecturers is aimed for participants who are lecturers in universities/institutes and colleges in India. This wi
From playlist Geometry and Topology for Lecturers
AlgTop9: Applications of Euler's formula and graphs
We use Euler's formula to show that there are at most 5 Platonic, or regular, solids. We discuss other types of polyhedra, including deltahedra (made of equilateral triangles) and Schafli's generalizations to higher dimensions. In particular in 4 dimensions there is the 120-cell, the 600-c
From playlist Algebraic Topology: a beginner's course - N J Wildberger
Archimedes Parabolic Area Formula for Cubics! | Algebraic Calculus One | Wild Egg
The very first and arguably most important calculation in Calculus was Archimedes' determination of the slice area of a parabola in terms of the area of a suitably inscribed triangle, involving the ratio 4/3. Remarkably, Archimedes' formula extends to the cubic case once we identify the ri
From playlist Old Algebraic Calculus Videos
Combinatorics and Geometry to Arithmetic of Circle Packings - Nakamura
Speaker: Kei Nakamura (Rutgers) Title: Combinatorics and Geometry to Arithmetic of Circle Packings Abstract: The Koebe-Andreev-Thurston/Schramm theorem assigns a conformally rigid fi-nite circle packing to a convex polyhedron, and then successive inversions yield a conformally rigid infin
From playlist Mathematics
The Archimedean Spiral | Visually Explained (animation code also explained)
This is a video explaining what is so extraordinary about Archimedes, and the geometric things he did back in the BC. This is a partial explanation of the topic, and a partially explaining the code. Timecodes: 0:00 - Intro 0:11 - Archimedean Spirals 3:40 - The Exhaustion Method 5:38 - Ma
From playlist ManimCE Tutorials 2021