A Challenging Problem of Rhombicuboctahedron by HCR

The picture above shows a rhombicuboctahedron having 24 identical vertices at each of which three square faces & one equilateral triangular face meet together. Calculate the correct value (upto three decimal points) of the solid angle (in Ste-radian) subtended by the (convex) solid at its vertex. Assumption: The eye of the observer is located exactly at any of 24 identical vertices of the above convex solid.