Uploaded December 2013 | Updated September 2026, 1 week ago
In this video you see the result of a rotation of the faces of a tetrahedron, somewhere halfway on the way becoming an octahedron.
When you rotate all the faces of any regular* or quasi regular* polyhedron (maybe even any convex* polyhedron with regular polygons as faces, but I'm not sure about that), until the corners of the polygons match, then you get a new polyhedron with more faces. When starting with a polyhedron that is not regular, then not necessarily all faces of the new polyhedron are regular however. For example, both a cube and an octahedron will become an cuboctahedron after rotating the faces and both a dodecahedron and an icosahedron will turn into the quasi regular isicosidodecahedron(12 dodecagons, 20 triangles). An isicosidodecahedron will turn into the quasi regular rhombicosidodecahedron(12 dodecagons, 20 triangles, 30 squares), which will turn into an irregular polyhedron with 12 dodecagons, 20 triangles, 30 squares and 60 times the same trapezium (Am. English: trapezoid) with 2 slanted edges of equal length.
*the 5 Platonic solids are the only regular polyhedra
*a quasi regular polyhedron has at least 2 different types of faces, they are known as Archimedian solids
*when you draw a line between any 2 points in a convex polyhedron, all the points on that line are part of that polyhedron.
In this video you see the result of a rotation of the faces of a tetrahedron, somewhere halfway on the way becoming an octahedron.
When you rotate all the faces of any regular* or quasi regular* polyhedron (maybe even any convex* polyhedron with regular polygons as faces, but I'm not sure about that), until the corners of the polygons match, then you get a new polyhedron with more faces. When starting with a polyhedron that is not regular, then not necessarily all faces of the new polyhedron are regular however. For example, both a cube and an octahedron will become an cuboctahedron after rotating the faces and both a dodecahedron and an icosahedron will turn into the quasi regular isicosidodecahedron(12 dodecagons, 20 triangles). An isicosidodecahedron will turn into the quasi regular rhombicosidodecahedron(12 dodecagons, 20 triangles, 30 squares), which will turn into an irregular polyhedron with 12 dodecagons, 20 triangles, 30 squares and 60 times the same trapezium (Am. English: trapezoid) with 2 slanted edges of equal length.
*the 5 Platonic solids are the only regular polyhedra
*a quasi regular polyhedron has at least 2 different types of faces, they are known as Archimedian solids
*when you draw a line between any 2 points in a convex polyhedron, all the points on that line are part of that polyhedron.
