Heptagonal prism
In geometry, the heptagonal prism is a prism with heptagonal base. This polyhedron has 9 faces, 21 edges, and 14 vertices.[1][2]
| 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.
Area
The area of a right heptagonal prism with height and with a side length of and apothem is given by:[1]
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:[1]
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 prisms | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Polyhedron |  |
 |
 |
 |
 |
|
 |
 |
 |
 |
 |
| Coxeter | |
 |
 |
 |
 |
|
 |
 |
 |
 |
 |
| Tiling |  |
 |
 |
 |
 |
 |
 |
 |
|||
| 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 |
gollark: Mostly, you just need to use a bunch of intermediate instances to receive, reduce and filter everything.
gollark: I mean, it's not like *all* the subjects died.
gollark: You *can*, but loading all the information - much of it conflicting - into your brain *has* been known to lead to a few moderately problematic side effects.
gollark: Now, while modern mindstate execution is fully deterministic, people aren't perfect judges of the "best" thing and there's some noise, so you probably want to use comparison counting sort or something.
gollark: You can either read aesthetic appreciation data out of their mindstates and rank that, or just use one per *comparison* instead.
References
- Sapiña, R. "Area and volume calculator of a heptagonal prism" (in Spanish). Problemas y ecuaciones. ISSN 2659-9899. Retrieved June 17, 2020.
- Pugh, Anthony (1976), Polyheda: A Visual Approach, University of California Press, p. 27, ISBN 9780520030565.
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.