How are platonic solids related?

Answer 1

One way in which Platonic solids are related is by duality. To construct the dual of a Platonic solid take the vertices of the dual to be the centres of the faces of the original. The lines joining adjacent centres of the original form the edges of the dual. In this way, the numbers of faces and vertices are swapped while the number of edges remain the same.

A tetrahedron is its own dual.

A hexahedron (cube) and octahedron from a dual pair.

A dodecahedron (cube) and icosahedron from a dual pair.

One way in which Platonic solids are related is by duality. To construct the dual of a Platonic solid take the vertices of the dual to be the centres of the faces of the original. The lines joining adjacent centres of the original form the edges of the dual. In this way, the numbers of faces and vertices are swapped while the number of edges remain the same.

A tetrahedron is its own dual.

A hexahedron (cube) and octahedron from a dual pair.

A dodecahedron (cube) and icosahedron from a dual pair.

One way in which Platonic solids are related is by duality. To construct the dual of a Platonic solid take the vertices of the dual to be the centres of the faces of the original. The lines joining adjacent centres of the original form the edges of the dual. In this way, the numbers of faces and vertices are swapped while the number of edges remain the same.

A tetrahedron is its own dual.

A hexahedron (cube) and octahedron from a dual pair.

A dodecahedron (cube) and icosahedron from a dual pair.

One way in which Platonic solids are related is by duality. To construct the dual of a Platonic solid take the vertices of the dual to be the centres of the faces of the original. The lines joining adjacent centres of the original form the edges of the dual. In this way, the numbers of faces and vertices are swapped while the number of edges remain the same.

A tetrahedron is its own dual.

A hexahedron (cube) and octahedron from a dual pair.

A dodecahedron (cube) and icosahedron from a dual pair.

Answer 2

One way in which Platonic solids are related is by duality. To construct the dual of a Platonic solid take the vertices of the dual to be the centres of the faces of the original. The lines joining adjacent centres of the original form the edges of the dual. In this way, the numbers of faces and vertices are swapped while the number of edges remain the same.

A tetrahedron is its own dual.

A hexahedron (cube) and octahedron from a dual pair.

A dodecahedron (cube) and icosahedron from a dual pair.