Elongated Square Pyramid

In geometry, the elongated square pyramid is one of the Johnson solids (). As the name suggests, it can be constructed by elongating a square pyramid () by attaching a cube to its square base. Like any elongated pyramid, it is topologically (but not geometrically) self-dual.

Formulae

The following formulae for the height ($H$), surface area ($A$) and volume ($V$) can be used if all faces are regular, with edge length $L$:
:$H = L\cdot \left( 1 + \frac\right) \approx L\cdot 1.707106781$
:$A = L^2 \cdot \left( 5 + \sqrt \right) \approx L^2\cdot 6.732050808$
:$V = L^3 \left( 1 + \frac\right)\approx L^3\cdot 1.23570226$

Dual polyhedron

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

Related polyhedra and honeycombs

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

See also

*Elongated square bipyramid

References

External links

*

{{Polyhedron-stub

Johnson solids
Self-dual polyhedra
Pyramids and bipyramids