http://www.ck12.org Chapter 11. Surface Area and Volume
F+V=E+ 2
6 +V= 10 + 2
V= 6 There are 6 vertices.Watch this video for help with the Examples above.
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Click image to the left for more content.CK-12 Foundation: Chapter11PolyhedronsB
Vocabulary
Apolyhedronis a 3-dimensional figure that is formed by polygons that enclose a region in space. Each polygon
in a polyhedron is aface.The line segment where two faces intersect is anedge.The point of intersection of two
edges is avertex.Aregular polyhedronis a polyhedron where all the faces are congruent regular polygons.
Guided Practice
- In a six-faced polyhedron, there are 10 edges. How many vertices does the polyhedron have?
- Markus counts the edges, faces, and vertices of a polyhedron. He comes up with 10 vertices, 5 faces, and 12
edges. Did he make a mistake? - Is this a polyhedron? Explain.
Answers:
- Solve forVin Euler’s Theorem.
F+V=E+ 2
6 +V= 10 + 2
V= 6
Therefore, there are 6 vertices.
- Plug all three numbers into Euler’s Theorem.
F+V=E+ 2
5 + 10 = 12 + 2
156 = 14
Because the two sides are not equal, Markus made a mistake.
- All of the faces are polygons, so this is a polyhedron. Notice that even though not all of the faces are regular
polygons, the number of faces, vertices, and edges still works with Euler’s Theorem.