with Minimum Partitional Area. 



511 



quadrilateral in the plane perpendicular to the four short 

 edges. It shows with mathematical accuracy (if we suppose 

 the wire edges infinitely thin) a complete quadrilateral, four 

 half-quadrilaterals, and four half- hexagons of the minimal 

 tetrakaidecahedron. The two principal views are represented 

 in figs. 5 and 6. 



16. The mathematical problem of calculating the forms of 

 the plane arc-edges, and of ihe curved surface of the hexa- 

 gonal faces, is easily carried out to any degree of approxima- 

 tion that may be desired ; though it would be very laborious, 

 and not worth the trouble, to do so further than a first ap- 

 proximation, as given in § 17 below. But first let us state 

 the rigorous mathematical problem ; which by symmetry 

 becomes narrowed to the consideration of a 60° sector BOB' 

 of our non-plane hexagon, bounded by straight lines C B, C B', 

 and a slightly curved edge B E B', in a plane, Q, through 



B B', inclined to the plane B C B' at an angle of tan -1 V% or 

 54° 44'. The plane of the curved edge I call Q, because it is 

 the plane of the contiguous quadrilateral. The mathematical 

 problem to be solved is to find the surface of zero curvature 

 edged by B C B' and cutting at 120° the plane Q all along the 

 inter sectional curve (fig. 7). It is obvious that this problem is 



