PPT-“Platonic Solids, Archimedean Solids, and Geodesic Sphere

Jim Olsen Western Illinois University JROlsenwiuedu Platonic Archimedean Plato 423 BC 347 BC Aristotle 384 BC  322 BC Euclid 325 and 265 BC Archimedes 287  BC . & Platonic Solids Vertices/Nodes: The common endpoint of two or more rays or line segments. Edges: the line segments where two surfaces meet Faces/Regions: Interior: area containing all the edge In Perspective. Symmetry and Regularity. Objects that are symmetrical look the same from several different views, or two sides are mirror images of each other.. Symmetric solids are referred to as regular, or Platonic solids.. Sebald. Geometric Solids. Introduction. Geometric Solids are 3-Dimensional (or “3-D”) shapes – which means they have the 3 . dimensions. of width, depth, and height. Basic examples are spheres, cubes, cylinders, and pyramids. But there are lots of others. Some geometric solids have . -Describe . these objects-. What are some things that you notice?. Have you ever seen anything like these? Where?. What do they remind you of?. How would you describe these objects?. How can we describe these using geometric terms?. MATH 420 Presentation: Kelly Burgess. What are they?. Convex Polyhedron (polyhedron: 3d solid with straight edges and flat faces). All faces are congruent. Same number of faces meet at each vertex. Named after Greek philosopher Plato who associated each with a basic "element". St Paul’s Geometry Masterclass I. Who are we?. Mairi Walker. Final year maths PhD student at The Open University. Studying links between geometry and numbers. A. lso interested in the history of maths. The molecular compounds like water, ammonia, and carbon dioxide have different physical properties because of the intermolecular forces.. Comparison of all three phases:. Liquids & Solids. Liquids & Solids. All . faces, all edges, all corners, are the . same.. They are . composed . of . regular 2D polygons:. There were infinitely many 2D n-. gons. !. How many of these regular 3D solids are there?. Making a Corner for a Platonic . Solids. Crystalline Solids- have a regular repeating arrangement of their particles.. Salts, Sugars, Metals. Amorphous Solids- have no regular repeating arrangement of their molecules. Common glass, several polymers.. Grade 9 Math. Platonic solids. E4 Make and apply generalizations about the properties of platonic solids. To prepare for this lesson. What is a polygon? . What are some polygons you know?. What is a regular polygon?. FROM MANURE DIGESTATE. Biocycle. REFOR 17. Portland OR. October 18, 2017. Craig Frear, PhD. Director of Research and Technology. Regenis. Examples of Fine Solids Separation Technologies. Use of gravitational forces, chemical flocculation, filtration, and/or pressure to separate suspended solids from wastewater—while using a variety of dewatering methods to produce a stackable solid product. . E-mail: . benzene4president@gmail.com. Web-site: http://clas.sa.ucsb.edu/staff/terri/. Liquids . and. . Solids – . ch.. 16. Liquids . and. . Solids – . ch.. 16. 1. Indicate the . types of forces. Investigating Regular Polyhedra– Level 1. What You’ll Learn…. What the Platonic solids are, what makes them unique, and how they relate to one another.. The math behind these special shapes and why there is a limited number of regular polyhedra. . Salts, Sugars, Metals. Amorphous Solids- have no regular repeating arrangement of their molecules. Common glass, several polymers.. Crystalline Structure. Amorphous. Amorphous solids. Amorphous solids, due to a lack of arrangement of molecules, .