▪ Dynamic Construction - Cuboctahedron

Dynamic Construction
The key-step of construction	Illustration
Start with a regular octahedron. Take the midpoints H, I, and G of segments AB, AC, and CD, respectively. Create two equ-triangles around line L through points H and G. Create a regular hexagon around line L through point I.
Create a convex polyhedron OEHIF. Take point J by central symmetry through point H of point F. Create an arc FJK. Create line M that is perpendicular to segments AB and OH.
Take a movable point P on arc FJK. Rotate the convex polyhedron OEHIF around line M mapping point F towards point P, then we get convex polyhedron R. Rotate R around line L mapping point H towards point Y to get convex polyhedron S. Rotate R around line L mapping point H towards point E to get convex polyhedron T.
Create three polyhedrons U, V, and W by central symmetry through point H of polyhedrons R, S, and  T, respectively. Please move point P from point F to point K; then we getCuboctahedron.

Πηγή: apollonius