A polyhedron is a three-dimensional solid assembled from polygonal faces meeting along edges and vertices.
A tetrahedron is the three-dimensional simplex, with four vertices, six edges, and four triangular faces.
Two edges of a tetrahedron are opposite when they share no vertex. The six edges split into three opposite pairs.
A Platonic solid is a convex polyhedron whose faces are congruent regular polygons and whose vertex figures are all alike.
The regular dodecahedron is the Platonic solid with 12 regular pentagonal faces, 20 vertices, and 30 edges.
An Archimedean solid is a convex uniform polyhedron with regular polygonal faces and equivalent vertices, allowing more than one type of face.
The icosidodecahedron has 20 triangular and 12 pentagonal faces, with the faces alternating around each of its 30 vertices. It can be obtained by cutting a dodecahedron through the midpoints of its edges.
