Dual polyhedron facts for kids
In geometry, every polyhedron is related to a dual polyhedron, where the vertices (points) of one polyhedron match with the faces (flat surfaces) of the other, and the edges connecting vertices in one polyhedron match with the edges connecting faces of the other. Starting with any given polyhedron, the dual of its dual is the original polyhedron.
For the five platonic polyhedra, only the tetrahedron is dual to itself. The cube and octahedron are dual, and the dodecahedron and icosahedron are dual.
Polyhedron  Vertices  Edges  Faces  Dual 

Tetrahedron  4  6  4  Tetrahedron 
Cube  8  12  6  Octahedron 
Octahedron  6  12  8  Cube 
Dodecahedron  20  30  12  Icosahedron 
Icosahedron  12  30  20  Dodecahedron 
 .
Images for kids

The dual of a cube is an octahedron. Vertices of one correspond to faces of the other, and edges correspond to each other.

The dual of a Platonic solid can be constructed by connecting the face centers. In general this creates only a topological dual. Images from Kepler's Harmonices Mundi (1619)
See also
In Spanish: Poliedro conjugado para niños