Hexagonal prism

 ( Prismatoid Polyhedra ) 

 of order 24
| type = prism,
[[parallelohedron]]
| dual = hexagonal bipyramid
     

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

---

As a semiregular polyhedron 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 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 dual polyhedron of a hexagonal prism is a hexagonal bipyramid.

The symmetry group of a right hexagonal prism is prismatic symmetry $D\_\{6\; \backslash mathrm\{h\}\}$ of order 24, consisting of rotation around an axis passing through the regular hexagon bases' center, and reflection across a horizontal plane.

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: $$V\; =\; \backslash frac\{3\; \backslash sqrt\{3\}\}\{2\}a^2h,$$ and its surface area is by summing the area of two regular hexagonal bases and the lateral faces of six squares: $$S\; =\; 3a(\backslash sqrt\{3\}a+2h).$$

---

As a parallelohedron The hexagonal prism is one of the parallelohedron, 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.

The hexagonal prism also exists as cells of four prismatic uniform convex honeycombs in 3 dimensions:

Triangular-hexagonal prismatic honeycomb	Snub triangular-hexagonal prismatic honeycomb	Rhombitriangular-hexagonal prismatic honeycomb

It also exists as cells of a number of four-dimensional uniform 4-polytopes, including:

truncated tetrahedral prism	truncated octahedral prism	Truncated cuboctahedral prism	Truncated icosahedral prism	Truncated icosidodecahedral prism
runcitruncated 5-cell	omnitruncated 5-cell	runcitruncated 16-cell	omnitruncated tesseract
runcitruncated 24-cell	omnitruncated 24-cell	runcitruncated 600-cell	omnitruncated 120-cell

---

External links

• Uniform Honeycombs in 3-Space VRML models
• The Uniform Polyhedra
• Virtual Reality Polyhedra The Encyclopedia of Polyhedra Prisms and antiprisms
• Hexagonal Prism Interactive Model -- works in your web browser

Post Comment