heptagonal prism

{{Short description|Prism with a 7-sided base}}

{{Infobox polyhedron

|image=Prism_7.png

|type=Uniform polyhedron

|faces=2 Heptagons
7 squares

|edges=21

|vertices=14

|coxeter={{CDD|node_1|7|node|2|node_1}}

|wythoff=2 7 | 2

|symmetry=D7h, [7,2], (*722), order 28

|rotation_group=D7, [7,2]+, (722), order 14

|vertex_config=7.4.4

|dual=Heptagonal bipyramid

|properties=Convex semiregular

|vertex_figure=Heptagonal prism vertfig.png

}}

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.{{cite web

|url=https://www.problemasyecuaciones.com/geometria3D/volumen/prisma/heptagonal/calculadora-area-volumen-formulas-demostracion.html

|title=Area and volume calculator of a heptagonal prism |last=Sapiña |first=R. |publisher=Problemas y ecuaciones |issn=2659-9899 |language=es

|access-date=June 17, 2020}}{{citation|title=Polyheda: A Visual Approach|first=Anthony|last=Pugh|publisher=University of California Press|year=1976|isbn=9780520030565|pages=27|url=https://books.google.com/books?id=IDDxpYQTR7kC&pg=PA21}}.

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:

:240px

Related polyhedra

{{UniformPrisms}}

References

{{Reflist}}