Planes and the Polyhedron: Definition and Example Video

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  • 0:05 What Is a Plane?
  • 0:58 What Is a Polyhedron?
  • 1:26 What Do They Look Like?
  • 1:55 Polyhedra in Real Life
  • 3:05 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Did you ever wonder what the pyramids in Egypt have to do with math? Watch this video to find out where in math a pyramid comes into play. Also, learn how flat, 2-dimensional shapes also come into play.

What Is a Plane?

First, what is a plane? It's not the type that flies overhead - the airplanes that transport people and things - but planes in math are flat surfaces that stretch out forever in all directions. It's like taking a piece of paper and imagining that the piece of paper never ended, that it has no edges.

Now, imagine punching all kinds of shapes out of our plane. Now, these shapes must have only straight edges, no curves of any kind. So, think of rectangles, squares, triangles, pentagons and the like; all of these flat shapes are pieces of a plane. These pieces are also called polygons because they have only straight edges.

What Is a Polyhedron?

When you connect several of these flat shapes and turn it into something 3-dimensional, then you have yourself a polyhedron. Defined, a polyhedron is a 3-dimensional object with flat, polygonal faces. What this means is that each side of the polyhedron is made up of one of our pieces from our plane. Each side is a polygon.

What Do They Look Like?

What do they look like? They can look similar to balls, except they have flat sides and edges and no curves. They can also look like ornaments that people hang up. Any 3-dimensional shape that you can create by gluing together polygons punched out of our plane is a polyhedron. Just remember that you have to glue all the pieces together; you can't have an open hole somewhere!

Polyhedra in Real Life

Where in real life will we see polyhedra? Here is where the pyramids of Egypt come into play. A pyramid has flat sides that are made up of polygons. The sides are triangles and the bottom is a square. That makes a pyramid a polyhedron!

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