Elongated square pyramid

The following formulae for the height (${\displaystyle H}$), surface area (${\displaystyle A}$) and volume (${\displaystyle V}$) can be used if all faces are regular, with edge length ${\displaystyle L}$:[2]

${\displaystyle H=L\cdot \left(1+{\frac {\sqrt {2}}{2}}\right)\approx L\cdot 1.707106781}$

${\displaystyle A=L^{2}\cdot \left(5+{\sqrt {3}}\right)\approx L^{2}\cdot 6.732050808}$

${\displaystyle V=L^{3}\left(1+{\frac {\sqrt {2}}{6}}\right)\approx L^{3}\cdot 1.23570226}$

The dual of the elongated square pyramid has 9 faces: 4 triangular, 1 square and 4 trapezoidal.

Dual elongated square pyramid	Net of dual

The elongated square pyramid can form a tessellation of space with tetrahedra,[3] similar to a modified tetrahedral-octahedral honeycomb.

• Elongated square bipyramid

• Weisstein, Eric W., "Johnson solid" ("Elongated square pyramid") at MathWorld.