Count Vertices, Edges, and Faces

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Count Vertices, Edges, and Faces

As stated previously, \(3D\) shapes, as well as objects, are distinct from \(2D\) shapes and objects due to the existence of the \(3\) dimensions – length, width (breadth), and height. Because of these \(3\) dimensions, these things have faces, edges, and vertices.

Related Topics

Faces

  • Faces refer to any one curved or flat surface of a solid item.
  • A \(3D\) shape could have one or more faces.

Edges

  • Edges are line segments on the boundary linking one vertex (corner point) to another one.
  • These act as a junction of \(2\) faces.

Vertices

  • A point where \(2\) or more lines meet up is known as a vertex.
  • It’s a corner.
  • The place edges intersect signifies the vertices.

The subsequent table displays the faces, edges, and vertices of some three-dimensional shapes (\(3D\) shapes).

\(3D\) shapesFacesEdgesVertices
Sphere\(1\)\(0\)\(0\)
Cylinder\(3\)\(2\)\(0\)
Cone\(2\)\(1\)\(1\)
Cube\(6\)\(12\)\(8\)
Rectangular Prism\(6\)\(12\)\(8\)
Triangular Prism\(5\)\(9\)\(6\)
Pentagonal Prism\(7\)\(15\)\(10\)
Hexagonal Prism\(8\)\(18\)\(12\)
Square Pyramid\(5\)\(8\)\(5\)
Triangular Pyramid\(4\)\(6\)\(4\)
Pentagonal Pyramid\(6\)\(10\)\(6\)
Hexagonal Pyramid\(7\)\(12\)\(7\)

Count Vertices, Edges, and Faces – Example 1:

Count Vertices, Edges, and Faces of this shape.

Solution:

This shape is a cube, so it has \(6\) faces, \(12\) edges and \(8\) vertices.

Count Vertices, Edges, and Faces – Example 2:

Count Vertices, Edges, and Faces of this shape.

Solution:

This shape is a cylinder, so it has \(3\) faces, \(2\) edges and \(0\) vertices.

Exercises for Counting Vertices, Edges, and Faces

Count Vertices, Edges, and Faces of these shapes.

1)

2)

This image has an empty alt attribute; its file name is answer-3.png

Answers

  1. \(\color{blue}{6,12,8}\)
  2. \(\color{blue}{8,18,12}\)

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