I am a shining prism of ivory. Six-eight-twelve my measure be. Pierced through am I by non-interesting prisms three, the longest being triangular on its face; the shortest being rectangular on its base; the third, isosceles trapezoidal in its face. The triangle measures three by four by five; the rectangle exactly two by five. The trapezoid is the strangest of them all. Its sides measure two, four, square root of two twice; quite irrational. What part of me is missing? For that is our quest: The ratio of what is missing to that of what is left

Solution:

The missing part is a trapezoid, Its sides measure two, three, square root of two twice