Icosahedron

Elementary School

Definition

An icosahedron is a solid polyhedron that consists of 20 faces, 30 sides, and 12 vertices. It is a platonic solid. Its name comes from the Greek word "icos-", which means twenty, and "-hedron", an Indo-European word that means seat.

Worked examples

\(F = 20, \; E = 30, \; V = 12\)

An icosahedron has 20 triangular faces, 30 edges, and 12 vertices, satisfying Euler's formula \(V - E + F = 2\).

Regular icosahedron: all 20 faces are equilateral triangles

When every face is the same size and shape, it is a Platonic solid with maximum symmetry.

Common mistakes

An icosahedron has 12 faces → An icosahedron has 20 faces Don't confuse it with a dodecahedron, which has 12 faces; 'icosa-' means twenty.
All polyhedra with 20 faces are icosahedra → An icosahedron specifically has 20 triangular faces and 12 vertices Other 20-faced solids exist but aren't icosahedra unless they match the vertex and edge count.
Thinking the icosahedron has square or pentagon faces → All 20 faces are triangles (equilateral in the regular icosahedron) The icosahedron is built entirely from triangular faces, not other polygons.

Where you'll use it next

You'll use icosahedra when studying Platonic solids in geometry, analyzing 3D symmetry groups, calculating surface area and volume of polyhedra, and in applications like molecular structures and game dice design.

Found in 1 StudyPug lesson

Mastering the Art of Classifying 3D Shapes

Grade 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.

5th Grade5th