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.^[1][2]

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Heptagonal prism
Type	Uniform polyhedron
Faces	2 Heptagons 7 squares
Edges	21
Vertices	14
Vertex configuration	7.4.4
Wythoff symbol	2 7 | 2
Coxeter diagram
Symmetry group	D7h, [7,2], (*722), order 28
Rotation group	D7, [7,2]+, (722), order 14
Dual polyhedron	Heptagonal bipyramid
Properties	Convex semiregular
Vertex figure

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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:^[1]

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

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:^[1]

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

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

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