All log diameters are equal; the planes of convergence pass through the diameters and intercept at the convergence vector.

     The geometry of the compound joint is that of a right circular cone. Equal ridge vectors, all at equal angles with respect to the convergence vector, lie on the nappe of the cone; the convergence vector is perpendicular to the inclined deck and lies on the altitude. The inclined deck is on the circular base.
     The points where the ridge vectors intercept the inclined deck are the vertices of a polygon, and this figure determines if a compound joint is feasible. If the outline is a triangle, a cyclic quadrilateral (i.e. the opposite angles are supplementary), or a regular polygon, a compound joint is possible. If the perpendicular bisectors of the sides of an irregular polygon intercept at a common point, this point is the center of a circle that circumscribes the shape, therefore the geometry is that of a compound joint.

     When three logs meet, the projection of the true deck to the inclined deck remains a triangle. Since a triangle can always be circumscribed, it follows that a joint comprised of three members may always be compound joined. An example of such a joint may be viewed in the PHOTO GALLERY 1 .