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?

Answer: 5/6

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