Cube and Octahedron Movement
Each vertex of a cube is connected to three vertices of an octahedron with bars. As you pull out the vertices of the octahedron, keeping the bar length constant, the size of the octahedron increases and the size of the cube decreases; if you push in the vertices, the opposite effects occur. A solid octahedron with constant size is also shown for reference. This can be built as a physical model if the bars are flexible enough to pass by each other and hinges are used at the vertices.
This Demonstration is based on an animation by R.W. Gray.
"Cube and Octahedron Movement"
Wolfram Demonstrations Project
Published: September 28 2007