The surface area of a right prism whose base is a regular n-sided polygon with side length s, and with height h, is therefore:

A right prism (with rectangular sides) with regular n-gon bases has Schläfli symbol { }×{n}. It approaches a cylinder as n approaches infinity.[6]

Prism definedexample

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The symmetry group of a right n-sided prism with regular base is Dnh of order 4n, except in the case of a cube, which has the larger symmetry group Oh of order 48, which has three versions of D4h as subgroups. The rotation group is Dn of order 2n, except in the case of a cube, which has the larger symmetry group O of order 24, which has three versions of D4 as subgroups.

Note: some texts may apply the term rectangular prism or square prism to both a right rectangular-based prism and a right square-based prism.

Example: a parallelepiped is an oblique prism whose base is a parallelogram, or equivalently a polyhedron with six parallelogram faces.

In geometry, a prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy (rigidly moved without rotation) of the first, and n other faces, necessarily all parallelograms, joining corresponding sides of the two bases. All cross-sections parallel to the bases are translations of the bases. Prisms are named after their bases, e.g. a prism with a pentagonal base is called a pentagonal prism. Prisms are a subclass of prismatoids.[2]

A crossed prism is a nonconvex polyhedron constructed from a prism, where the vertices of one base are inverted around the center of this base (or rotated by 180°). This transforms the side rectangular faces into crossed rectangles. For a regular polygon base, the appearance is an n-gonal hour glass. All oblique edges pass through a single body center. Note: no vertex is at this body centre. A crossed prism is topologically identical to an n-gonal prism.

The volume of a prism whose base is an n-sided regular polygon with side length s is therefore: V = n 4 h s 2 cot ⁡ π n . {\displaystyle V={\frac {n}{4}}hs^{2}\cot {\frac {\pi }{n}}.}

The key though, is, if you have a parfocal lens, use it to shoot at the hyperfocal distance (again, good old Wikipedia can help with an explanation of this - http://en.wikipedia.org/wiki/Hyperfocal_distance ) at a wider aperture than usual in landscapes. This gets us away from f22 and f16 down to sharper apertures like f13 and f11 - while still maintaining front to back sharpness. Many pro's, like David Noton, use this. Look at the technical info on many of his landscapes and they are shot at f11.

Prism definedin math

It is very convenient to focus at the maximum focal length and change the zoom afterwards. It is more important for manual-focus lens because a well functioning auto-focus can quickly adjust the lens to keep it in focus.

Parfocal lens is a lens which remains in focus when you change the focal length. The non-parfocal lens is called varifocal.

I have noticed that most of the parfocal lenses have zoom ratios of 3:1. Maybe this holds the answer: in my study of photography, lenses that have a zoom ratio of 3:1, 2:1, and 1:1 have better quality compared to higher lens ratios, because they produce less chromatic aberration. In my opinion, parfocal lenses have are better since their aberration is less compared to lenses that have zoom ratios of 4:1 or higher.

A star prism is a nonconvex polyhedron constructed by two identical star polygon faces on the top and bottom, being parallel and offset by a distance and connected by rectangular faces. A uniform star prism will have Schläfli symbol {p/q} × { }, with p rectangles and 2 {p/q} faces. It is topologically identical to a p-gonal prism.

Parfocal lenses remain in focus when you change the focal length as previously stated. They are most useful for movie/video work - it's awkward to keep having to pull focus as your zoom changes.

Regular duoprisms are represented as {p}×{q}, with pq vertices, 2pq edges, pq square faces, p q-gon faces, q p-gon faces, and bounded by p q-gonal prisms and q p-gonal prisms.

Prism definedsynonym

The hosohedra and dihedra also possess dihedral symmetry, and an n-gonal prism can be constructed via the geometrical truncation of an n-gonal hosohedron, as well as through the cantellation or expansion of an n-gonal dihedron.

Triangularprism defined

A prismatic polytope is a higher-dimensional generalization of a prism. An n-dimensional prismatic polytope is constructed from two (n − 1)-dimensional polytopes, translated into the next dimension.

Higher order prismatic polytopes also exist as cartesian products of any two or more polytopes. The dimension of a product polytope is the sum of the dimensions of its elements. The first examples of these exist in 4-dimensional space; they are called duoprisms as the product of two polygons in 4-dimensions.

Prismmeaning in Hindi

Like many basic geometric terms, the word prism (from Greek πρίσμα (prisma) 'something sawed') was first used in Euclid's Elements. Euclid defined the term in Book XI as “a solid figure contained by two opposite, equal and parallel planes, while the rest are parallelograms”. However, this definition has been criticized for not being specific enough in regard to the nature of the bases (a cause of some confusion amongst generations of later geometry writers).[3][4]

A twisted prism cannot be dissected into tetrahedra without adding new vertices. The simplest twisted prism has triangle bases and is called a Schönhardt polyhedron.

Take an n-polytope with Fi i-face elements (i = 0, ..., n). Its (n + 1)-polytope prism will have 2Fi + Fi−1 i-face elements. (With F−1 = 0, Fn = 1.)

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A regular n-polytope represented by Schläfli symbol {p,q,...,t} can form a uniform prismatic (n + 1)-polytope represented by a Cartesian product of two Schläfli symbols: {p,q,...,t}×{ }.

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Types ofprism

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See also 'focus breathing', where a change in the focus changes the apparent focal length slightly. Again this is something it's nice to avoid in movie/video work. In general the more you pay, the less they breathe...

Lens design is always a series of trade-offs, if money, size and weight are no object you can build a lens that will be parfocal, fast and have high quality optically. So in the movie business they end up with lenses like this: http://www.flickr.com/photos/mrmitch/2185341989/in/photostream

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A right prism is a prism in which the joining edges and faces are perpendicular to the base faces.[5] This applies if and only if all the joining faces are rectangular.

The volume of a prism is the product of the area of the base by the height, i.e. the distance between the two base faces (in the case of a non-right prism, note that this means the perpendicular distance).

I heard someone say that after using a parfocal lens for the first time, they would never switch back. What is a parfocal lens, how is it different from any other lens, and what are the advantages and disadvantages for photography? Would you pay extra for this or prefer it over varifocal?

What isprismin Physics

Thus all the faces of a uniform prism are regular polygons. Also, such prisms are isogonal; thus they are uniform polyhedra. They form one of the two infinite series of semiregular polyhedra, the other series being formed by the antiprisms.

transitive verb (Physics & Astron.) To render parallel to a certain line or direction; to bring into the same line, as the axes of telescopes, etc.; to render ...

A twisted prism is a nonconvex polyhedron constructed from a uniform n-prism with each side face bisected on the square diagonal, by twisting the top, usually by ⁠π/n⁠ radians (⁠180/n⁠ degrees) in the same direction, causing sides to be concave.[8][9]

An n-gonal twisted prism is topologically identical to the n-gonal uniform antiprism, but has half the symmetry group: Dn, [n,2]+, order 2n. It can be seen as a nonconvex antiprism, with tetrahedra removed between pairs of triangles.

Prismshape

The prismatic n-polytope elements are doubled from the (n − 1)-polytope elements and then creating new elements from the next lower element.

A toroidal prism is a nonconvex polyhedron like a crossed prism, but without bottom and top base faces, and with simple rectangular side faces closing the polyhedron. This can only be done for even-sided base polygons. These are topological tori, with Euler characteristic of zero. The topological polyhedral net can be cut from two rows of a square tiling (with vertex configuration 4.4.4.4): a band of n squares, each attached to a crossed rectangle. An n-gonal toroidal prism has 2n vertices, 2n faces: n squares and n crossed rectangles, and 4n edges. It is topologically self-dual.

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For example, {4}×{4}, a 4-4 duoprism is a lower symmetry form of a tesseract, as is {4,3}×{ }, a cubic prism. {4}×{4}×{ } (4-4 duoprism prism), {4,3}×{4} (cube-4 duoprism) and {4,3,3}×{ } (tesseractic prism) are lower symmetry forms of a 5-cube.

A truncated prism is formed when prism is sliced by a plane that is not parallel to its bases. A truncated prism's bases are not congruent, and its sides are not parallelograms.[7]

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A frustum is a similar construction to a prism, with trapezoid lateral faces and differently sized top and bottom polygons.