Английская Википедия:Heptagonal prism

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Шаблон:Short description Шаблон:Infobox polyhedron

Файл:Prisma heptagonal 3D.stl
3D model of a (uniform) 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.[1][2]

Area

The area of a right heptagonal prism with height <math>h</math> and with a side length of <math>L</math> and apothem <math>a_p</math> is given by:[1]

<math>A = 7L\cdot (a_p + h)</math>

Volume

The volume is found by taking the area of the base, with a side length of <math>L</math> and apothem <math>a_p</math>, and multiplying it by the height <math>h</math>, giving the formula:[1]

<math>V = \frac{7}{2}\cdot h\cdot L\cdot a_p</math>

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:

Файл:Spherical heptagonal prism.svg

Related polyhedra

Шаблон:UniformPrisms

References

Шаблон:Reflist

External links


Шаблон:Polyhedron-stub