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How many vertices, edges, and faces of the polyhedron are there? List them.

There are 10 vertices:. A , B , C , D , E , F , G , H , I , and J . There are 15 edges:. AF, BG, CH, DI, EJ, AB, BC, CD, DE, EA, FG, GH, HI, IJ, and JF. There are 7 faces:. pentagons: ABCDE and FGHIJ , and quadrilaterals: ABGF , BCHG , CDIH , DEJI , and EAFJ.

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How many vertices, edges, and faces of the polyhedron are there? List them.

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  1. There are 10 vertices: A, B, C, D, E, F, G, H, I, and J. There are 15 edges: AF, BG, CH, DI, EJ, AB, BC, CD, DE, EA, FG, GH, HI, IJ, and JF. There are 7 faces: pentagons: ABCDE and FGHIJ, and quadrilaterals: ABGF, BCHG, CDIH, DEJI, and EAFJ Space Figures and Cross Sections LESSON 11-1 Additional Examples How many vertices, edges, and faces of the polyhedron are there? List them. Quick Check

  2. Space Figures and Cross Sections LESSON 11-1 Additional Examples Use Euler’s Formula to find the number of edges of a polyhedron with 6 faces and 8 vertices. F+V= E+ 2 Euler’s Formula 6 + 8 = E+ 2 Substitute the number of faces and vertices. 12 = ESimplify. A solid with 6 faces and 8 vertices has 12 edges. Quick Check

  3. Draw a net. Space Figures and Cross Sections LESSON 11-1 Additional Examples Use the pentagonal prism from Example 1 to verify Euler’s Formula. Then draw a net for the figure and verify Euler’s Formula for the two-dimensional figure. Use the faces F = 7, vertices V = 10, and edges E = 15. F+V= E+ 2 Euler’s Formula 7 + 10 = 15 + 2 Substitute the number of faces and vertices. Count the regions: F = 7 Count the vertices: V = 18 Count the segments: E = 24 F + V = E + 1 Euler’s Formula in two dimensions 7 + 18 = 24 + 1 Substitute. Quick Check

  4. Space Figures and Cross Sections LESSON 11-1 Additional Examples Describe this cross section. The plane is parallel to the triangular base of the figure, so the cross section is also a triangle. Quick Check

  5. Space Figures and Cross Sections LESSON 11-1 Additional Examples Draw and describe a cross section formed by a vertical plane intersecting the top and bottom faces of a cube. If the vertical plane is parallel to opposite faces, the cross section is a square. Sample: If the vertical plane is not parallel to opposite faces, the cross section is a rectangle. Quick Check

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