Icosahedron

An icosahedron is a polyhedron with 20 faces. The name commonly denotes the regular convex solid whose faces are equilateral triangles.

Polyhedron: A three-dimensional solid bounded by flat polygonal faces, straight edges, and vertices. An icosahedron is one specific kind of polyhedron, defined by having 20 faces.
Platonic solid: A convex regular polyhedron whose faces are congruent regular polygons and whose vertex arrangements are identical. The regular icosahedron is one of the five Platonic solids.
Tetrahedron: A polyhedron with four triangular faces, four vertices, and six edges. It is the simplest Platonic solid, with far fewer faces than the icosahedron.
Icosahedral virus: A virus whose capsid has icosahedral symmetry, built from repeated protein subunits. Many viruses use this arrangement to enclose genetic material with a small set of proteins.
Equilateral triangle: A triangle with three equal sides and three equal angles. Each face of the regular convex icosahedron is an equilateral triangle.
Icosahedral graph: The graph formed by the vertices and edges of an icosahedron. It captures the regular icosahedron's connectivity without representing its faces as surfaces.
Octahedron: A Platonic solid with eight equilateral-triangle faces, six vertices, and twelve edges. It shares triangular faces with the icosahedron but has a different vertex arrangement.
C60 fullerene: A carbon molecule of 60 atoms arranged in a truncated-icosahedral cage. Its carbon cage derives from an icosahedron whose vertices are truncated.
Vertex configuration: A description of the arrangement of polygonal faces meeting at each vertex of a polyhedron. Five triangular faces meet at every vertex of a regular icosahedron.
Dual polyhedron: A polyhedron formed by placing a vertex in each original face and joining vertices across shared edges. The dual of the regular icosahedron is the dodecahedron.

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