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Exploring 3-D shapes!

Exploring 3-D shapes! . Glasses not required!. Polyhedra !. A polyhedron is a 3-dimensional, closed object whose surface is made up of polygons. Common examples: cubes and pyramids. Are these polyhedra ?. Things We Can Count . Faces – the polygons on the outside of the polyhedron.

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Exploring 3-D shapes!

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  1. Exploring 3-D shapes! • Glasses not required!

  2. Polyhedra! • A polyhedron is a 3-dimensional, closed object whose surface is made up of polygons. • Common examples: cubes and pyramids

  3. Are these polyhedra?

  4. Things We Can Count • Faces – the polygons on the outside of the polyhedron. • Edges – the lines that touch polygons to each other. • Vertices – the “corners” that connect edges to other edges

  5. Most Fun Example – Soccer Ball • 32 faces (20 hexagons, 12 pentagons) • 60 vertices (each connected to 2 hexagons and one pentagon) • 90 edges

  6. Our goal: • Count the number of faces, edges, and vertices on each of the following polyhedra: • Cube • Triangular pyramid • Square pyramid

  7. And These Things:

  8. What These All Share: • Try and come up with a formula that relates the numbers of edges, faces, and vertices of a certain polyhedron, and see if it works for EVERY polyhedron. • Something maybe like: E + F = ????

  9. Euler’s Polyhedron Formula:

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