Friday, September 18, 2015
Unizor - Geometry3D - Cuboctahedron
Unizor - Creative Minds through Art of Mathematics - Math4Teens
Given a cube ABCDA'B'C'D'. We cut-off all its vertices as follows.
Let points P, Q and R be midpoints of, correspondingly, edges AB, AD and AA'. The plane going through these three points cuts-off a triangular pyramid APQR from our cube.
Similar procedure we perform for each remaining vertex. The remaining solid after all these cuts is cuboctahedron.
What is the ratio of a volume of remaining part of a cube (cuboctahedron) to its original volume?