Faces, Edges And Vertices of 3D Shapes Examples
Example 1: Verify Euler’s formula for the heptahedron.
Solution:
A heptahedron has 7 faces, 10 vertices, and 15 edges.
From Euler’s formula, we have,
F + V = 2 + E
⇒ 7 + 10 = 2 + 15
⇒ 17 = 17
Hence, Euler’s formula is verified for the heptahedron.
Example 2: Calculate the number of edges of a polyhedron if it has 6 vertices and 9 faces.
Solution:
Given data,
V = 6 and F = 5
From Euler’s formula, we have,
F + V = 2 + E
⇒ 5 + 6 = 2 + E
⇒ 11 = 2 + E
⇒ E = 11 – 2 = 9
Hence, the given polyhedron has 9 edges.
Example 3: Calculate the number of vertices of a polyhedron if it has 5 faces and 8 edges.
Solution:
Given data,
F = 5 and E = 8
From Euler’s formula, we have,
F + V = 2 + E
⇒ 5 + V = 2 + 8
⇒ 5 + V = 10
⇒ V = 10 – 5 = 5
Hence, the given polyhedron has 5 vertices.
Faces, Edges And Vertices of 3D Shapes
Faces, Edges, And Vertices of 3D Shapes: Faces, Edges, and Vertices are the three basic properties that are used to define various 3D objects. They have different dimensions like length, width, and height.
Faces are the flat surfaces of a 3D shape. They are bounded by edges and are what give the shape its appearance. Edges are the straight lines where two faces of a 3D shape meet. They form the boundaries between faces and help define the shape’s overall structure. Vertices (singular: vertex) are the points where the edges of a 3D shape meet. They are essentially the corners of the shape.
In this article, we are going to learn about the faces, edges, and vertices of different 3D shapes in detail.
Table of Content
- What are Faces?
- What are Edges?
- What are Vertices?
- Types of Polyhedron
- Faces, Edges And Vertices of 3D Shapes
- Euler’s Formula
- Relation Between Faces, Edges And Vertices of 3D Shapes
- Faces, Edges And Vertices of 3D Shapes Examples
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