Let A B C of Fig. 424 be the elevation of the pyramid, and E F G of Fig. 425 the plan. From the center K draw the lines E K, F K and G K in the plan, representing the angles or hips of the pyramid. From the point K erect K H, perpendicular to F K and equal in length to the hight of the pyramid, as shown by A D of the elevation. Draw the hypothenuse F H, which then represents the length of the corner lines.

Fig. 421. - Elevation.

Fig. 425. - Plan.

Fig. 426. - Pattern.

The Envelope of a Triangular Pyramid.

From any point, as L of Fig. 426, for center, with radius equal to F H. describe the arc MN OI indefinitely, and draw L M. From M set off the chord M N, in length equal to the side F G of the plan. In like manner set off N O and O I respectively, equal to G E and E F of the plan. Connect I and L, as shown, and draw L O and L N. Then L I O N M is the pattern sought.