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### Problem Statement **5)** For a regular hexahedron, find the number of faces, vertices, and edges in the polyhedron. Then verify Euler's equation for that polyhedron. ### Explanation A regular hexahedron is another term for a cube. A cube has: - **Number of Faces (F)**: 6 - **Number of Vertices (V)**: 8 - **Number of Edges (E)**: 12 Euler's formula for polyhedra states that for any convex polyhedron: \[ V - E + F = 2 \] Let's verify Euler's equation for the cube: Given: - \( V = 8 \) - \( E = 12 \) - \( F = 6 \) Substitute these values into Euler's formula: \[ V - E + F = 8 - 12 + 6 = 2 \] Therefore, Euler's equation holds true for a regular hexahedron (cube).

### Problem Statement **5)** For a regular hexahedron, find the number of faces, vertices, and edges in the polyhedron. Then verify Euler's equation for that polyhedron. ### Explanation A regular hexahedron is another term for a cube. A cube has: - **Number of Faces (F)**: 6 - **Number of Vertices (V)**: 8 - **Number of Edges (E)**: 12 Euler's formula for polyhedra states that for any convex polyhedron: \[ V - E + F = 2 \] Let's verify Euler's equation for the cube: Given: - \( V = 8 \) - \( E = 12 \) - \( F = 6 \) Substitute these values into Euler's formula: \[ V - E + F = 8 - 12 + 6 = 2 \] Therefore, Euler's equation holds true for a regular hexahedron (cube).

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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### Problem Statement **5)** For a regular hexahedron, find the number of faces, vertices, and edges in the polyhedron. Then verify Euler's equation for that polyhedron. ### Explanation A regular hexahedron is another term for a cube. A cube has: - **Number of Faces (F)**: 6 - **Number of Vertices (V)**: 8 - **Number of Edges (E)**: 12 Euler's formula for polyhedra states that for any convex polyhedron: \[ V - E + F = 2 \] Let's verify Euler's equation for the cube: Given: - \( V = 8 \) - \( E = 12 \) - \( F = 6 \) Substitute these values into Euler's formula: \[ V - E + F = 8 - 12 + 6 = 2 \] Therefore, Euler's equation holds true for a regular hexahedron (cube).
Transcribed Image Text:### Problem Statement **5)** For a regular hexahedron, find the number of faces, vertices, and edges in the polyhedron. Then verify Euler's equation for that polyhedron. ### Explanation A regular hexahedron is another term for a cube. A cube has: - **Number of Faces (F)**: 6 - **Number of Vertices (V)**: 8 - **Number of Edges (E)**: 12 Euler's formula for polyhedra states that for any convex polyhedron: \[ V - E + F = 2 \] Let's verify Euler's equation for the cube: Given: - \( V = 8 \) - \( E = 12 \) - \( F = 6 \) Substitute these values into Euler's formula: \[ V - E + F = 8 - 12 + 6 = 2 \] Therefore, Euler's equation holds true for a regular hexahedron (cube).
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