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In [[geometry]], a '''prismatoid''' is a [[polyhedron]] where all [[vertex (geometry)|vertices]] lie in two parallel planes.  (If both planes have the same number of vertices,
and the lateral faces are either [[parallelogram]]s or [[trapezoid]]s, it is called a '''prismoid'''.)


If the areas of the two parallel faces are A<sub>1</sub> and A<sub>3</sub>, the cross-sectional area of the intersection of the prismatoid with a plane midway between the two parallel faces is A<sub>2</sub>, and the height (the distance between the two parallel faces) is h, then the [[volume]] of the prismatoid is given by <math>V = \frac{h(A_1 + 4A_2 + A_3)}{6}</math> (This formula follows immediately by [[integral|integrating]] the area parallel to the two planes of vertices by [[Simpson's rule]], since that rule is exact for integration of [[polynomial]]s of degree up to 3, and in this case the area is at most a [[quadratic function]] in the height.)


== Prismatoid families ==
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[[Image:Pentagonal pyramid.png|100px]]
[[Image:Pentagonal prism.png|100px]]
[[Image:Pentagonal_antiprism.png|100px]]
[[Image:Pentagrammic crossed antiprism.png|100px]]
[[Image:Pentagonal cupola.png|100px]]
[[Image:Pentagonal frustum.svg|100px]]
 
Families of prismatoids include:
 
* [[Pyramid (geometry)|Pyramids]], where one plane contains only a single point;
* [[Wedge (geometry)|Wedges]], where one plane contains only two points;
* [[Prism (geometry)|Prisms]], where the polygons in each plane are congruent and joined by rectangles or parallelograms;
* [[Antiprism]]s, where the polygons in each plane are congruent and joined by an alternating strip of triangles;
* [[Crossed antiprism]]s;
* [[cupola (geometry)|Cupolae]], where the polygon in one plane contains twice as many points as the other and is joined to it by alternating triangles and rectangles;
* [[Frustum|Frusta]] obtained by [[Truncation (geometry)|truncation]] of a pyramid;
* [[Quadrilateral]]-faced [[Hexahedron|hexahedral]] prismatoids:
*# [[Parallelepiped]]s - six [[parallelogram]] faces
*# [[Rhombohedron]]s - six [[rhombus]] faces
*# [[Trigonal trapezohedron|Trigonal trapezohedra]] - six congruent rhombus faces
*# [[Cuboid]]s - six rectangular faces
*# [[frustum|Quadrilateral frusta]] - an [[Apex (geometry)|apex]]-[[Truncation (geometry)|truncated]] [[square pyramid]]
*# [[Cube]]s - six square faces
 
== Higher dimensions ==
 
In general a [[polytope]] is prismatoidal if its vertices exist in two [[hyperplane]]s. For example in 4-dimension, two polyhedra can be placed in 2 parallel 3-spaces, and connected with polyhedral sides.
 
[[File:4D Tetrahedral Cupola-perspective-cuboctahedron-first.png|320px]]<BR>A tetrahedral-cuboctahedral cupola.
 
==External links==
* {{MathWorld | urlname=Prismatoid | title=Prismatoid}}
 
{{Polyhedron navigator}}
 
{{polyhedron-stub}}
[[Category:Polyhedra]]
[[Category:Prismatoid polyhedra]]

Revision as of 00:11, 28 February 2014


When spending time outdoors is not an option, spending time in a hotel suite can be equally relaxing and fun. Booking a hotel was simple, because rooms for a family of four are always easy to find. 4)What was your relationship with Anissa Jones like during and after the series. The underlying philosophy from your schooling may vary depending on whether it is a government school, a religious school, or one of the alternate schooling systems. A root canal is necessary when the tissue in the root chamber of the tooth becomes infected. Yes, pack your stroller so you can circle the deck.

Dealing with difficult people goes beyond working with difficult people but often means trying to handle frustrating and distressing family members. Currently, the company operates at over 370 sites, including 135 factories, in 68 countries worldwide and generates annual revenues of $28 billion. Just be sure you get free quotes from numerous companies before selecting yours so you can find the most affordable and the most effective for your specific security requirements. There are resources to help you, such as the report “Real Life Guidance: Finding More Family Time. Then, choose one word (a sight word or other familiar word) that doesn't belong holiday [linode02.wandborg.se] in the word family. The 6 way I told above is not all the way you can do to strengthen your relationship with family.

Don't worry you can give it back with the thorough cleaning if the carpet. Higher salaries allow families to consider day care, special after school programs, or nannies. For example, no one wants to hurt Cousin Dee’s expectations about hosting the Thanksgiving feast. You can't head to the movies because everyone needs a potty break at one time or another and some of you like to talk through the show. You'll also notice that they start telling lies saying they are working late when they are really stopping off at the pub for a drink. If the box doesn't already have an opening in the front cut out a mouth and make jagged teeth.

It does not really matter which type of car that you choose. If the client gives you the freedom of graphic design then you have a great chance to show your creativity and ideas but make sure, you don't go personal. What is so sad is that young people today just are not into camping. Let go, give them the space they have demanded and get on with living your life. (Example: I'm thinking of a number between'Skip count by 2's, 3's, 4's'). The television show 'Sharknado' might be closer to a sequel than Hollywood originally predicted.

When you are in the market to sell a single family home that you have been renting out for investment, it is an easier task since your pool of buyers are both investors as well as people who are looking to purchase homes for themselves. It may be considered as contempt of court when family court orders are broken. If God is involved things will always fare far better. Although it seems like a strange idea at first, it is a great craze that has caught on across the world -- having begun it's journey in Australia, and just recently launched here in the UK with The - Sticker - Family. Top 10 Reasons Why It's Easier To Buy A $5,000,000 Apartment Building Than A Single Family Investment Property. Ganesha, on the other hand, simply folded his palms in prayer and walked around his seated parents, returning to his starting point ahead of Kartikeya.