Heptagonal prism

Short description: Prism with a 7-sided base

Heptagonal prism
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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

File:Prisma heptagonal 3D.stl 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 $h$ and with a side length of $L$ and apothem $a_p$ is given by:

$A=7L\cdot (a_p+h)$

Volume

The volume is found by taking the area of the base, with a side length of $L$ and apothem $a_p$, and multiplying it by the height $h$, giving the formula:

$V=\frac{7}{2}\cdot h\cdot L\cdot a_p$

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:

External links

• Weisstein, Eric W.. "Prism". http://mathworld.wolfram.com/Prism.html.