In a regular hip or hip end, a crown rafter receives into the end of the ridge board, sitting precisely in the centre of the span of the wall plates. Geometrically speaking, assuming the pitch is the same on all planes of the roof, the true length of the crown rafter from the wall plate to the geometric centre of the hip/ridge intersection is identical to the true length of the common rafters. When drawn on paper this can be seen clearly. A 45 degree line coming away from the corner of the wall plates represents the hip rafter. A line representing the crown rafter moves down the centre span of the roof. Another line is drawn perpendicular to the crown rafter, equidistant from the corner of the wall plate, representing the last common rafter. Where these three lines meet is the geometric centre of the hip intersection. The position of the last common rafter is offset by half the thickness of the crown rafter, back towards the corner of the wall plates. The outside face of the last common rafter also signals the end of the ridge board, creating a suitable surface for the crown rafter to meet. Therefore, the actual length of the crown rafter is the true length of the common rafters, less half the thickness of itself. In a modern setting in which we utilise 2” timbers in all aspects of the roof, the apex of the intersection following this rule gives us a beautifully simple receptacle for the hip top cut. This being said, even in more traditional scenarios in which ridge boards were often much thinner, this same rule of subtracting half the thickness of the ridge board gives us a good intersection to receive the hip top cut.