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The gyroelongated square dipyramid is one of the eight convex deltahedra built up from 16 equilateral
triangles. It consists of two oppositely faced square
pyramids rotated 
to each other and separated by a 4-antiprism.
It is Johnson solid 
.
If the centroid is at the origin and the sides are of unit length, the equations of the 4-antiprism give
height of the middle points
as 
.
Adding the height of the square
pyramids gives apex heights of 
. The surface
area and volume of the solid are
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(1)
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(2)
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(3)
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