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Geometric Solids

Geometric Solids. By Daniel J. Sebald. Introduction.

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Geometric Solids

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  1. Geometric Solids By Daniel J. Sebald

  2. 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 faces that are flat, curved, or both. Some have faces that are all the same shape. Some have faces that are different shapes. But they all have 3 dimensions. Cylinder Cube Sphere Pyramid

  3. What are Dimensions? To understand what “3 dimensional” means, you have to understand what a dimension is. The dictionary defines “dimension” as “a measurement of length in one direction.” But that doesn’t really help. It’s easier to understand what it is by looking at examples. A point has no dimensions. A line has 1 dimension because you can only measure it in one direction. A figure drawn on a piece of paper can be measured in 2 directions, so it is 2 dimensional. Finally, a solid can be measured in 3 directions, so it is 3 dimensional.

  4. Types of Geometric Solids: Polyhedra and Non-Polyhedra Solids come in 2 types: polyhedra and non-polyhedra. Non-polyhedradescribes any geometric solid that has any surface that is not flat, like a sphere, cone, or cylinder. cylinder cone sphere torus

  5. Polyhedra and Non-Polyhedra Polyhedra describes a geometric solid that has all flat faces, but the faces don’t have to be the same size or shape. Polyhedra must have at least 4 faces but there is no limit to how many faces they can have. Some examples of polyhedra are pictured below: Truncated dodecahedron Pentagonal prism Truncated tetrahedron Rhombicuboctahedron Truncated cube Pentagonal prism

  6. Truncated What? Some of the Polyhedra are called Truncated. Truncated means that something is cut off. In a truncated polyhedra, the corners, called “vertices,” are cut off and replaced with a new face. For example, a truncated cube has new triangle shaped faces where the cube’s vertices were. The shape of the original polyhedra will determine the shape of the new face in each vertex. The pictures below show a cube, and then a truncated cube. Cube Truncated Cube

  7. A Platonic Solid is a special type of Polyhedra, in which each face is exactly the same, and the same number of faces meet at each corner, or vertex. They were named after a famous philosopher and mathematician from ancient Greece named “Plato.” Platonic Solids

  8. Platonic Solids Amazingly, there are only 5 geometric solids that qualify as platonic solids.

  9. The Five Platonic Solids Cube Dodecahedron Tetrahedron Octahedron Icosahedron

  10. Vocabulary Words Dimension: a measurement of length in one direction Edge: the line where faces of a geometric solid meet Face: an individual surface of a geometric solid Non-Polyhedra: a geometric solid that has any surface that is not flat Platonic solid: a polyhedra whose faces are all exactly the same, and the same number of faces meet at each vertex Polyhedra: a geometric solid that has all flat faces Truncate: to cut off the vertices of a geometric sold and replace them with a new face. Vertices: corners of geometric solid (singular is vertex)

  11. Quiz Part 1 – Match the platonic solids to their names Platonic Solids Names a. b. c. d. e. _____ icosahedron _____ dodecahedron _____ cube _____ tetrahedron _____ octahedron

  12. Quiz – Part 2 1. How many sides does an icosahedron have? _________ 2. Is a soccer ball shaped like a a. truncated icosahedron b. truncated dodecahedron c. truncated cube 3. What is a vertex? _____________

  13. Answers Platonic Solids Names a. b. c. d. e. __e__ icosahedron __d__ dodecahedron _a___ cube _b___ tetrahedron _c___ octahedron

  14. Answers 1. How many sides does an icosahedron have? ___20____ 2. Is a soccer ball shaped like a a. truncated icosahedron b. truncated dodecahedron c. truncated cube 3. What is a vertex? __a corner________

  15. Bibliography Algebra & Geometry – Anything But square. Green, Dan. 2011. Interactives – 3D Shapes www.learner.org/interactives/geometry January 29, 2013. Platonic Solids www.mathisfun.com/platonic_solids.html January 28, 2013. Understanding Mathematics. Alfeld, Peter. January 22, 1997. Platonic Solids http://mathworld.wolfram.com/platonicsolid.html January 29, 2013

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