Hexagonal prism

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title: "Hexagonal prism" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["prismatoid-polyhedra", "space-filling-polyhedra", "zonohedra"] description: "Prism with a 6-sided base" topic_path: "general/prismatoid-polyhedra" source: "https://en.wikipedia.org/wiki/Hexagonal_prism" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0

::summary Prism with a 6-sided base ::

::data[format=table title="infobox polyhedron"]

Field	Value
image	Hexagonal Prism.svg
name	Hexagon prism
symmetry	prismatic symmetry D_{6\mathrm{h
::

| image = Hexagonal Prism.svg | name = Hexagon prism | symmetry = prismatic symmetry D_{6\mathrm{h}} of order 24 | type = prism, parallelohedron | dual = hexagonal bipyramid ::figure[src="https://upload.wikimedia.org/wikipedia/commons/9/99/Prisma_hexagonal_3D.stl" caption="3D model of a uniform hexagonal prism"] ::

In geometry, the hexagonal prism is a prism with hexagonal base. this polyhedron has 8 faces, 18 edges, and 12 vertices.

Properties

A hexagonal prism has twelve vertices, eighteen edges, and eight faces. Every prism has two faces known as its bases, and the bases of a hexagonal prism are hexagons. The hexagons has six vertices, each of which pairs with another hexagon's vertex, forming six edges. These edges form three parallelograms as other faces. A prism is said to be right if the edges are of the same length and perpendicular to the base.

If faces are all regular, the hexagonal prism is a semiregular polyhedron—more generally, a uniform polyhedron—and the fourth in an infinite set of prisms formed by square sides and two regular polygon caps. It can be seen as a truncated hexagonal hosohedron, represented by Schläfli symbol t{2,6}. Alternately it can be seen as the Cartesian product of a regular hexagon and a line segment, and represented by the product {6}×{}. The symmetry group of a right hexagonal prism is prismatic symmetry D_{6 \mathrm{h}} of order 24, consisting of rotation around an axis passing through the regular hexagon bases' center, and reflection across a horizontal plane.{{citation | last1 = Flusser | first1 = J. | last2 = Suk | first2 = T. | last3 = Zitofa | first3 = B. | year = 2017 | title = 2D and 3D Image Analysis by Moments | publisher = John Wiley & Sons | isbn = 978-1-119-03935-8 | url = https://books.google.com/books?id=jwKLDQAAQBAJ&pg=PA126 | page = 126

As in most prisms, the volume is found by taking the area of the base, with a side length of a , and multiplying it by the height h, giving the formula: V = \frac{3 \sqrt{3}}{2}a^2h, and its surface area is by summing the area of two regular hexagonal bases and the lateral faces of six squares: S = 3a(\sqrt{3}a+2h).

Honeycombs

::figure[src="https://upload.wikimedia.org/wikipedia/commons/d/db/Hexagonal_prismatic_honeycomb.png" caption="Hexagonal prismatic honeycomb"] ::

The hexagonal prism is one of the parallelohedra, a polyhedral class that can be translated without rotations in Euclidean space, producing honeycombs; this class was discovered by Evgraf Fedorov in accordance with his studies of crystallography systems. The hexagonal prism is generated from four line segments, three of them parallel to a common plane and the fourth not. Its most symmetric form is the right prism over a regular hexagon, forming the hexagonal prismatic honeycomb.{{citation | last1 = Delaney | first1 = Gary W. | last2 = Khoury | first2 = David | date = February 2013 | doi = 10.1140/epjb/e2012-30445-y | issue = 2 | journal = The European Physical Journal B | title = Onset of rigidity in 3D stretched string networks | volume = 86| page = 44 | bibcode = 2013EPJB...86...44D

The hexagonal prism also exists as cells of four prismatic uniform convex honeycombs in 3 dimensions: ::data[format=table] | [[File:Triangular-hexagonal_prismatic_honeycomb.png|100px]] | [[File:Snub triangular-hexagonal prismatic honeycomb.png|100px]] | [[File:Rhombitriangular-hexagonal prismatic honeycomb.png|100px]] | |---|---|---| ::

It also exists as cells of a number of four-dimensional uniform 4-polytopes, including: ::data[format=table] | [[File:24-cell t0123 F4.svg|100px]] | [[File:24-cell t013 F4.svg|100px]] | [[File:120-cell_t023_H3.png|100px]] | [[File:120-cell_t0123_H3.png|100px]] | |---|---|---|---| ::

References

References

1. Pugh, Anthony. (1976). "Polyhedra: A Visual Approach". University of California Press.
2. Wheater, Carolyn C.. (2007). "Geometry". Career Press.
3. Alexandrov, A. D.. (2005). "Convex Polyhedra". Springer.

::callout[type=info title="Wikipedia Source"] This article was imported from Wikipedia and is available under the Creative Commons Attribution-ShareAlike 4.0 License. Content has been adapted to SurfDoc format. Original contributors can be found on the article history page. ::