## Gyroelongated Square Dipyramid

One of the eight convex Deltahedra. It consists of two oppositely faced Square Pyramids rotated 45° to each other and separated by a ribbon of eight side-to-side Triangles. It is Johnson Solid .

Call the coordinates of the upper Pyramid bases (± 1, ± 1, ) and of the lower (, 0, ) and (0, , ). Call the Pyramid apexes (0, 0, ). Consider the points (1, 1, 0) and (0, 0, ). The height of the Pyramid is then given by

 (1)

 (2)

Now consider the points (1, 1, ) and (, 0, ). The height of the base is given by

 (3)

 (4)

so
 (5) (6)