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Heptagonal prism

From Wikipedia, the free encyclopedia
Heptagonal prism
TypeUniform polyhedron
Faces2 Heptagons
7 squares
Edges21
Vertices14
Vertex configuration7.4.4
Wythoff symbol2 7 | 2
Coxeter diagram
Symmetry groupD7h, [7,2], (*722), order 28
Rotation groupD7, [7,2]+, (722), order 14
Dual polyhedronHeptagonal bipyramid
PropertiesConvex 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

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The area of a right heptagonal prism with height and with a side length of and apothem is given by:[1]

Volume

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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

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

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Family of uniform n-gonal prisms
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

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  1. ^ a b c 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.
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