http://www.ck12.org Chapter 11. Surface Area and Volume
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.
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Complete the table using Euler’s Theorem.
TABLE11.1:
Name Faces Edges Vertices- Rectangular Prism 6 12
- Octagonal Pyramid 16 9
- Regular
Icosahedron
20 12
- Cube 12 8
- Triangular Pyramid 4 4
- Octahedron 8 12
- Heptagonal Prism 21 14
- Triangular Prism 5 9
Determine if the following figures are polyhedra. If so, name the figure and find the number of faces, edges, and
vertices.