Elongated pentagonal pyramid

Template:Short description Template:Infobox polyhedron File:J9 elongated pentagonal pyramid.stl

In geometry, the elongated pentagonal pyramid is one of the Johnson solids (Template:Math). As the name suggests, it can be constructed by elongating a pentagonal pyramid (Template:Math) by attaching a pentagonal prism to its base.

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 $L$:

$H=L\cdot (1+\sqrt{\frac{5-\sqrt{5}}{10}})\approx L\cdot 1.525731112$

$A=L^2\cdot \frac{20+5\sqrt{3}+\sqrt{25+10\sqrt{5}}}{4}\approx L^2\cdot 8.88554091$

$V=L^3\cdot \left(\frac{5+\sqrt{5}+6\sqrt{25+10\sqrt{5}}}{24}\right)\approx L^3\cdot 2.021980233$

Dual polyhedron

The dual of the elongated pentagonal pyramid has 11 faces: 5 triangular, 1 pentagonal and 5 trapezoidal. It is topologically identical to the Johnson solid.

Dual elongated pentagonal pyramid	Net of dual

See also

• Elongated pentagonal bipyramid

External links

• Template:Mathworld2