In the geometry of hyperbolic 3-space, the octahedron-dodecahedron honeycomb is a compact uniform honeycomb, constructed from dodecahedron, octahedron, and icosidodecahedron cells, in a rhombicuboctahedron vertex figure. It has a single-ring Coxeter diagram, , and is named by its two regular cells. A geometric honeycomb is a space-filling of polyhedral or higher-dimensional cells, so that there are no gaps. It is an example of the more general mathematical tiling or tessellation in any number of dimensions. Honeycombs are usually constructed in ordinary Euclidean ("flat") space, like the convex uniform honeycombs. They may also be constructed in non-Euclidean spaces, such as hyperbolic uniform honeycombs. Any finite uniform polytope can be projected to its circumsphere to form a uniform honeycomb in spherical space. (Wikipedia).
How to Construct a Dodecahedron
How the greeks constructed the Dodecahedron. Euclids Elements Book 13, Proposition 17. In geometry, a dodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagons as faces, which is a Platonic solid. A regular dode
From playlist Platonic Solids
Canonical structures inside the Platonic solids III | Universal Hyperbolic Geometry 51
The dodecahedron is surely one of the truly great mathematical objects---revered by the ancient Greeks, Kepler, and many mathematicians since. Its symmetries are particularly rich, and in this video we look at how to see the five-fold and six-fold symmetries of this object via internal str
From playlist Universal Hyperbolic Geometry
How to construct an Octahedron
How the greeks constructed the 2nd platonic solid: the regular octahedron Source: Euclids Elements Book 13, Proposition 14. In geometry, an octahedron is a polyhedron with eight faces, twelve edges, and six vertices. The term is most commonly used to refer to the regular octahedron, a Plat
From playlist Platonic Solids
Canonical structures inside Platonic solids II | Universal Hyperbolic Geometry 50 | NJ Wildberger
The cube and the octahedron are dual solids. Each has contained within it both 2-fold, 3-fold and 4-fold symmetry. In this video we look at how these symmetries are generated in the cube via canonical structures. Along the way we discuss bipartite graphs. This gives us more insight into t
From playlist Universal Hyperbolic Geometry
This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/19O1
From playlist 3D printing
Available from Shapeways: https://www.shapeways.com/shops/henryseg?section=Holonomy+mazes Thanks to Sabetta Matsumoto and Chaim Goodman-Strauss for building the sculpture, to Saul Schleimer for naming the "rook", and to all of them for helpful conversations.
From playlist 3D printing
How do ceramic crystal structures differ from metal crystal structures?
Metal crystal structures are much simpler than ceramic structures. This is due to two reasons. First, ceramics have positive and negative charged ions. Cations and ions must maintain charge neutrality. Second, the size of cations and anions are very different! Structures with multiple diff
From playlist Materials Sciences 101 - Introduction to Materials Science & Engineering 2020
The remarkable Platonic solids II: symmetry | Universal Hyperbolic Geometry 48 | NJ Wildberger
We look at the symmetries of the Platonic solids, starting here with rigid motions, which are essentially rotations about fixed axes. We use the normalization of angle whereby one full turn has the value one, and also connect the number of rigid motions with the number of directed edges.
From playlist Universal Hyperbolic Geometry
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
Instruction to download http://singingbanana.com/popupdodecahedron.pdf More information about the dodecahedron that I would have like to have gone into in this video http://uk.youtube.com/watch?v=-lqpSpje42o Dodecahedron at wikipedia http://en.wikipedia.org/wiki/Dodecahedron Plato
From playlist My Maths Videos
mse 3310 spring 2017 midterm 2 review
From playlist Introduction to Ceramics Spring 2017
Day 14 ceramic crystal structures
0:00 reading quiz 5:25 HCP structure and close-packing 10:27 theoretical density calculation 15:00 difference between observed and theoretical densities 18:16 ceramic crystal structures and using rc/ra ratio to determine coordination 23:26 rock salt (NaCl) structure 29:28 cesium chloride (
From playlist Introduction to Materials Science and Engineering Fall 2017
0:00 coordination of hexagonal close-packed HCP structure 4:40 theoretical density 21:37 structure of ceramics using cation/anion ratio 30:65 NaCl rock salt structure 33:05 CsCl structure 35:18 ZnS zinc blende structure 39:00 solving for lattice parameter in terms of cation and anion radii
From playlist Introduction to Materials Science & Engineering Fall 2019
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
Coordination Compounds: Geometry and Nomenclature
We have been learning a lot about a wide variety of compounds, but we haven't really looked much at the transition metals. These also form compounds called coordination compounds, and the types of bonds involved in these compounds is quite a bit different from what we are used to, as are t
From playlist General Chemistry
Role of Magnetoelastic Coupling in Kitaev Materials by Roser Valenti
PROGRAM FRUSTRATED METALS AND INSULATORS (HYBRID) ORGANIZERS: Federico Becca (University of Trieste, Italy), Subhro Bhattacharjee (ICTS-TIFR, India), Yasir Iqbal (IIT Madras, India), Bella Lake (Helmholtz-Zentrum Berlin für Materialien und Energie, Germany), Yogesh Singh (IISER Mohali, In
From playlist FRUSTRATED METALS AND INSULATORS (HYBRID, 2022)
From playlist Linear Algebra Ch 6
Henry Segerman - 3D Shadows: Casting Light on the Fourth Dimension - 02/11/17
Henry Segerman "3D Shadows: Casting Light on the Fourth Dimension" February 11, 2017 Wesier Hall Ann Arbor, Michigan
From playlist 3D printing
SU(4) Dirac Fermions on Honeycomb Lattice by Basudeb Mondal
DISCUSSION MEETING : APS SATELLITE MEETING AT ICTS ORGANIZERS : Ranjini Bandyopadhyay (RRI, India), Subhro Bhattacharjee (ICTS-TIFR, India), Arindam Ghosh (IISc, India), Shobhana Narasimhan (JNCASR, India) and Sumantra Sarkar (IISc, India) DATE & TIME: 15 March 2022 to 18 March 2022 VEN
From playlist APS Satellite Meeting at ICTS-2022
Chemistry - Molecular Structure (10 of 45) Basic Shapes-Octahedral with Free Electron Pairs
This video has an uploading audio error...the audio error-free video lives at: https://www.youtube.com/watch?v=IAULFewncc8 In this video I will explain the octahedral with free electron pair(s).
From playlist CHEMISTRY 14 MOLECULAR STRUCTURE