Explanation Euler’s Formula: For any polyhedron that doesn’t intersect itself, F+V-E = 2 Where F = number of faces, V = number of vertices, E = number of edges. Given: Table 13: Name V F E Tetrahedron 4 4 6 Cube 8 6 12 Octahedron 6 8 12 Dodecahedron

A Problem Solving Approach to Mathematics for Elementary School Teachers, Books a la Carte Edition plus NEW MyLab Math with Pearson eText - Access Card Package (12th Edition)

12th Edition

ISBN: 9780133865479

Author: Rick Billstein, Shlomo Libeskind, Johnny Lott

Publisher: PEARSON

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Chapter 11, Problem 13NT

To determine

To Write:

Euler’s formula and verify that the relationship holds for the three truncated polyhedra in figure 56 using table 13.

Name V F E

Tetrahedron 4 4 6

Cube 8 6 12

Octahedron 6 8 12

Dodecahedron 20 12 30

Icosahedron 12 20 30

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Chapter 11, Problem 12NT

Chapter 12.1, Problem 1MC

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Chapter 11 Solutions

A Problem Solving Approach to Mathematics for Elementary School Teachers, Books a la Carte Edition plus NEW MyLab Math with Pearson eText - Access Card Package (12th Edition)

Ch. 11.1 - Answer each of the following and explain your...Ch. 11.1 - Given a line and a point not on the line, explain...Ch. 11.1 - How are pairs of parallel lines and skew lines a....Ch. 11.1 - Is it possible for ABC to have vertex C? Why?Ch. 11.1 - If planes and are distinct planes having points...Ch. 11.1 - Prob. 7MC Ch. 11.1 - MATHEMATICAL CONNECTIONS A line n is perpendicular...Ch. 11.1 - MATHEMATICAL CONNECTIONS a. Sketch three rays that...Ch. 11.1 - Identify a physical object within the classroom to...Ch. 11.1 - Prob. 12MC

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Name	V	F	E
Tetrahedron	4	4	6
Cube	8	6	12
Octahedron	6	8	12
Dodecahedron	20	12	30
Icosahedron	12	20	30

Euler’s formula and verify that the relationship holds for the three truncated polyhedra in figure 56 using table 13. Name V F E Tetrahedron 4 4 6 Cube 8 6 12 Octahedron 6 8 12 Dodecahedron 20 12 30 Icosahedron 12 20 30

Solution Summary: The author explains that the three truncated polyhedra in figure 56 satisfies the Euler’s formula.

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To Write: Euler’s formula and verify that the relationship holds for the three truncated polyhedra in figure 56 using table 13. Name V F E Tetrahedron 4 4 6 Cube 8 6 12 Octahedron 6 8 12 Dodecahedron 20 12 30 Icosahedron 12 20 30

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Chapter 11 Solutions

To Write:

Euler’s formula and verify that the relationship holds for the three truncated polyhedra in figure 56 using table 13.

Name V F E

Tetrahedron 4 4 6

Cube 8 6 12

Octahedron 6 8 12

Dodecahedron 20 12 30

Icosahedron 12 20 30