Heptagonal prism

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

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 ${\displaystyle h}$ and with a side length of ${\displaystyle L}$ and apothem ${\displaystyle a_{p}}$ is given by: ^[1]

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

Volume

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.

Images

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

Related polyhedra

Family of uniform n-gonal prisms v t e
Prism name	Digonal prism	(Trigonal) Triangular prism	(Tetragonal) Square prism	Pentagonal prism	Hexagonal prism	Heptagonal prism	Octagonal prism	Enneagonal prism	Decagonal prism	Hendecagonal prism	Dodecagonal prism	...	Apeirogonal prism
Polyhedron image												...
Spherical tiling image												Plane tiling image
Vertex config.	2.4.4	3.4.4	4.4.4	5.4.4	6.4.4	7.4.4	8.4.4	9.4.4	10.4.4	11.4.4	12.4.4	...	∞.4.4
Coxeter diagram												...

References

1. Sapiña, R. "Area and volume calculator of a heptagonal prism" (in Spanish). Problemas y ecuaciones. ISSN   2659-9899 . Retrieved June 17, 2020.
2. Pugh, Anthony (1976), Polyheda: A Visual Approach, University of California Press, p. 27, ISBN   9780520030565 .

External links

• Weisstein, Eric W. "Prism". MathWorld .