PPT-The (regular, 3D) Platonic 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 . & 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.. Module 1. Session Topics. Surfaces and Solids of Revolution. Degree of Revolution. Hollow Objects. Visualizing Revolution. Surfaces and Solids of Revolution. Surfaces and Solids of Revolution are formed when a 2-D shape is revolved about an axis. th. Dimension – and beyond!. The Power and Beauty of Geometry. Carlo. . Heinrich. . Séquin. University of California, Berkeley. Basel, Switzerland. Math Institute, dating back to 15. th. century. -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?. ● . Phases and Phase Diagrams. ● Liquids and Liquid Properties. ● Intermolecular Forces. ● Heating Curves. ● Introduction to Solids. ● Cubic Packing Arrangements. ● Closest-Packed Structures. Jim Olsen. Western Illinois University. JR-Olsen@wiu.edu. Platonic ~ Archimedean. Plato. (423 BC –347 BC). Aristotle. (384 BC – 322 BC). Euclid. (325 and 265 BC). Archimedes . (. 287.  BC –. 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?. Geometry. Chapter 12. This Slideshow was developed to accompany the textbook. Larson Geometry. By Larson. , R., Boswell, L., . Kanold. , T. D., & Stiff, L. . 2011 . Holt . McDougal. Some examples and diagrams are taken from the textbook.. Lecture Presentation. Classifying Solids Based on Bonds. Metallic solids. are held together by a “sea” of collectively shared electrons.. Ionic solids. are sets of cations and anions mutually attracted to one another.. Chapter 3 REGULAR LANGUAGES AND REGULAR GRAMMARS Learning Objectives At the conclusion of the chapter, the student will be able to: Identify the language associated with a regular expression Find a regular expression to describe a given language 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. . DOWNLOAD Platonic Architectonics Platonic 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, .