Heptagonal prism

In geometry, the heptagonal prism is a prism with heptagonal base. This polyhedron has 9 faces (2 bases and 7 sides), 21 edges, and 14 vertices.

Area

The area of a right heptagonal prism with height ${\displaystyle h}$ and with a side length of ${\displaystyle L}$ and apothem ${\displaystyle a_{p}}$ is given by:

${\displaystyle A=7L\cdot (a_{p}+h)}$

Volume

The volume is found by taking the area of the base, with a side length of ${\displaystyle L}$ and apothem ${\displaystyle a_{p}}$, and multiplying it by the height ${\displaystyle h}$, giving the formula:

${\displaystyle V={\frac {7}{2}}\cdot h\cdot L\cdot a_{p}}$

This formula also works for the oblique prism due to the Cavalieri's principle.

Images

The heptagonal prism can also be seen as a tiling on a sphere:

Related polyhedra

References

External links

• Weisstein, Eric W. "Prism". MathWorld.