Polyhedral compounds

Compound of six tetrahedra

The compound of six tetrahedra is a uniform polyhedron compound. It's composed of a symmetric arrangement of 6 tetrahedra. It can be constructed by inscribing a stella octangula within each cube in the compound of three cubes, or by stellating each octahedron in the compound of three octahedra. It is one of only five polyhedral compounds (along with the compound of two great dodecahedra, the compound of five great dodecahedra, the compound of two small stellated dodecahedra, and the compound of five small stellated dodecahedra) which is vertex-transitive and face-transitive but not edge-transitive. (Wikipedia).

Compound of six tetrahedra
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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

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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

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Chemistry - Molecular Structure (4.5 of 45) Basic Shapes - Tetrahedral Molecules

Visit http://ilectureonline.com for more math and science lectures! In this video I will introduce the basic tetrahedral molecules of the molecular structure.

From playlist CHEMISTRY 14 MOLECULAR STRUCTURE

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Chemistry - Liquids and Solids (32 of 59) Crystal Structure: Seven Types of Unit Cells

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the 7 types of unit cells.

From playlist CHEMISTRY 16 LIQUIDS AND SOLIDS

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SuperFrabjous

The mathematics underlying a geometric puzzle/sculpture. The plastic version shown at the end of the video is not yet commercially available.

From playlist Other Geometric Sculpture

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Chemistry - Molecular Structure (4 of 45) Basic Shapes - Tetrahedral Molecules

Visit http://ilectureonline.com for more math and science lectures! In this video I will introduce the basic tetrahedral molecules of the molecular structure.

From playlist CHEMISTRY 14 MOLECULAR STRUCTURE

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Writing Chemical Formulas For Covalent Molecular Compounds

This chemistry video tutorial explains the process of writing chemical formulas for covalent molecular compounds using prefixes such as mono, di, tri, and tetra. This video contains plenty of examples and practice problems of naming binary covalent molecular compounds. New Chemistry Vide

From playlist New AP & General Chemistry Video Playlist

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Using a set of points determine if the figure is a parallelogram using the midpoint formula

👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr

From playlist Quadrilaterals on a Coordinate Plane

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Triple Integrals: Find the Volume of a Tetrahedron Given the Vertices

This video explains how to determine the volume of a tetrahedron using a triple integral given the vertices of the tetrahedron. http://mathispower4u.com

From playlist Triple Integrals

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Silicate crystal structures

Silicate minerals are very common. There are many different structures that include silicate tetrahedra (SiO4)^(4-) building blocks. These blocks can be three dimensionall corner-shared as in quartz cristobalite, isolated as in forsterite, sharing one corner between two tetrahedra as in Ak

From playlist Materials Sciences 101 - Introduction to Materials Science & Engineering 2020

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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

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26. Van't Hoff's Tetrahedral Carbon and Chirality

Freshman Organic Chemistry (CHEM 125) With his tetrahedral carbon models van't Hoff explained the mysteries of known optical isomers possessing stereogenic centers and predicted the existence of chiral allenes, a class of molecules that would not be observed for another sixty-one years. S

From playlist Freshman Organic Chemistry with J. Michael McBride

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MagLab Theory Winter School 2019: Collin Broholm

Topic: Spin fluctuations in strongly correlated electron systems The National MagLab held it's seventh Theory Winter School in Tallahassee, FL from January 7th - 11th, 2019.

From playlist 2019 Theory Winter School

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Journée de la Revue d’histoire des mathématiques - Veronica Gavagna - 01/12/17

Journée de la Revue d’histoire des mathématiques (séance préparée par la rédaction de la RHM) Veronica Gavagna (Università degli Studi di Firenze), « Studies on regular polyhedra in the Renaissance: the case of Francesco Maurolico » ---------------------------------- Vous pouvez nous re

From playlist Séminaire d'Histoire des Mathématiques

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Lecture 17

Chemistry 1B Professor Eric Potma Department of Chemistry University of California, Irvine

From playlist Chem 1P: Studio Version

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Dipole-Octupole Quantum Spin Liquids inCe-based Phrochlores by Bruce D. Gaulin

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)

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Mod-01 Lec-13 Surface Effects and Physical properties of nanomaterials

Nanostructures and Nanomaterials: Characterization and Properties by Characterization and Properties by Dr. Kantesh Balani & Dr. Anandh Subramaniam,Department of Nanotechnology,IIT Kanpur.For more details on NPTEL visit http://nptel.ac.in.

From playlist IIT Kanpur: Nanostructures and Nanomaterials | CosmoLearning.org

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10. Structure-based feature vector

Chemistry alone isn't enough to help ML models make predictions. Instead, we need to featurize the structure of a material. What aspects would make good structural features? How do we featurize them? This video covers some relevant structural features from the atomic through the crystal st

From playlist Materials Informatics

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Lecture 19

Chemistry 1B Professor Eric Potma Department of Chemistry University of California, Irvine

From playlist Chem 1P: Studio Version

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Three space-filling shapes hiding in the structure of diamond

Diamond is an arrangement of carbon atoms called the diamond cubic structure. As well as the cubes there are two other space-filling shapes that are found within it. In the unit cell I say "three more inside". It should of course be "four more inside". https://en.wikipedia.org/wiki/Diamo

From playlist Geometry

Related pages

Compound of three cubes | Compound of two great dodecahedra | Compound of three octahedra | Compound of five great dodecahedra | Subgroup | Symmetry group | Compound of five small stellated dodecahedra | Truncated octahedron | Octahedral symmetry | Uniform polyhedron compound | Convex hull | Dihedral symmetry in three dimensions | Stellation | Tetrahedron | Compound of two small stellated dodecahedra