A geometry problem by Anthony PhamGeometry Level 4
Observe net \(ABCDEFGHIJ\).
Figure \(BEGJ\) is a unit square, with angle \(ABJ=90^\circ\) and \(BJ=AB=BC\). Also, \(DE=EF=FG=GH\) and \(CE=AJ=JI\), with the ratio of \(GH\) to \(IJ\) is \(1:2\). The net is to form a closed polyhedron no holes or overlaps. If the volume is written as a fraction in lowest terms, find the sum of the numerator and the denominator.