heptagonal prism
{{Short description|Prism with a 7-sided base}}
{{Infobox polyhedron
|image=Prism_7.png
|type=Uniform polyhedron
|edges=21
|vertices=14
|coxeter={{CDD|node_1|7|node|2|node_1}}
|wythoff=
|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
}}
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
Volume
The volume is found by taking the area of the base, with a side length of and apothem , and multiplying it by the height , giving the formula:
:
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
{{UniformPrisms}}
References
{{Reflist}}