Edge of a Polyhedron
Elementary School
Definition
Where the faces of a polyhedron intersect with one another. These edges join together the polyhedron. The number of edges can be found using Euler's polyhedral formula which tells us that V + F - E = 2. V stands for vertices, F is for faces, and E is for edges.
Worked examples
\(V + F - E = 2 \)→\( 8 + 6 - E = 2 \)→\( E = 12\)
A cube has 8 vertices and 6 faces, so Euler's formula gives 12 edges.
\(V + F - E = 2 \)→\( 5 + 5 - E = 2 \)→\( E = 8\)
A square pyramid has 5 vertices and 5 faces, so it has 8 edges.
Common mistakes
- \(V + F - E = 2 \)→\( 6 + 8 - E = 2 \)→\( E = 12\) → \(V + F - E = 2 \)→\( 8 + 6 - E = 2 \)→\( E = 12\) For a cube, V = 8 vertices (corners) and F = 6 faces; students often swap these values.
- Counting each edge twice where faces meet → Each edge is shared by exactly two faces but counted once An edge is the single line segment where two faces intersect; don't double-count it.
- \(E = V + F\) → \(E = V + F - 2\) Euler's formula rearranges to E = V + F - 2, not V + F.
Where you'll use it next
You'll use edges when classifying polyhedra, calculating surface area and volume, and studying nets. Euler's formula appears again in topology and graph theory in advanced math courses.
Found in 1 StudyPug lesson
Mastering the Art of Classifying 3D Shapes
5th Grade5thGrade 5 Math placeholder
Dive into the fascinating world of 3D shapes! Learn to identify and classify prisms, pyramids, and curved surfaces. Enhance your spatial reasoning and geometry skills with our comprehensive guide.
See also
Reviewed by Pat Cheng, M.Ed. — StudyPug Curriculum Lead · Last updated June 6, 2026