Laplace–Runge–Lenz vector: Difference between revisions

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{{Semireg dual polyhedra db|Semireg dual polyhedron stat table|dtT}}
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In [[geometry]], a '''triakis tetrahedron''' is an [[Archimedean solid|Archimedean dual]] solid, or a [[Catalan solid]]. Its dual is the [[truncated tetrahedron]].
 
It can be seen as a [[tetrahedron]] with [[triangular pyramid]]s added to each face; that is, it is the [[Kleetope]] of the tetrahedron. This interpretation is expressed in the name.
 
If the triakis tetrahedron has shorter edge lengths 1, it has area <math>\tfrac{5}{3} \scriptstyle{\sqrt{11}}</math> and volume <math>\tfrac{25}{36} \scriptstyle{\sqrt{2}}</math>.
 
== Orthogonal projections ==
{| class=wikitable
|+ [[Orthogonal projection]]
!Centered by
!Edge normal
!Face normal
!Edge
!Face/vertex
|- align=center
!Truncated<BR>[[tetrahedron]]
|[[File:tetrahedron t01 ae.png|100px]]
|[[File:tetrahedron t01 af36.png|100px]]
|[[File:3-simplex t01.svg|100px]]
|[[File:3-simplex t01 A2.svg|100px]]
|- align=center
!Triakis<BR>tetrahedron
|[[File:Dual tetrahedron t01 ae.png|100px]]
|[[File:Dual tetrahedron t01 af36.png|100px]]
|[[File:Dual tetrahedron t01.png|100px]]
|[[File:Dual tetrahedron t01 A2.png|100px]]
|- align=center
|- align=center
!Projective<BR>symmetry
![1]
![1]
![3]
![4]
|}
 
==Variations==
A triakis tetrahedron with equilateral triangle faces represents a [[polyhedral net|net]] of the four-dimensional regular polytope known as the [[5-cell]].
 
==Stellations==
:[[File:Stellation of triakis tetrahedron.png|160px]]
This chiral figure is one of thirteen [[stellation]]s allowed by [[The Fifty-Nine Icosahedra#Miller's rules|Miller's rules]].
 
== Related polyhedra ==
The triakis tetrahedron is a part of a sequence of polyhedra and tilings, extending into the hyperbolic plane. These [[face-transitive]] figures have (*n32) reflectional [[Orbifold notation|symmetry]].
 
{{Truncated figure1 table}}
 
{{Tetrahedron family}}
 
==See also==
*[[Truncated triakis tetrahedron]]
 
==References==
*{{The Geometrical Foundation of Natural Structure (book)}} (Section 3-9)
*{{Citation |last1=Wenninger |first1=Magnus |author1-link=Magnus Wenninger |title=Dual Models |publisher=[[Cambridge University Press]] |isbn=978-0-521-54325-5 |id={{MathSciNet |id=730208}} |year=1983}} (The thirteen semiregular convex polyhedra and their duals, Page 14, Triakistetrahedron)
*''The Symmetries of Things'' 2008, John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, ISBN 978-1-56881-220-5 [http://www.akpeters.com/product.asp?ProdCode=2205] (Chapter 21, Naming the Archimedean and Catalan polyhedra and tilings, page 284, Triakis tetrahedron )
 
==External links==
*{{Mathworld2 |urlname=TriakisTetrahedron |title=Triakis tetrahedron |urlname2=CatalanSolid |title2=Catalan solid}}
 
{{Polyhedron navigator}}
 
[[Category:Catalan solids]]
 
 
{{Polyhedron-stub}}

Latest revision as of 18:34, 7 January 2015

Baby blankets not only give warmth, but also comfort. It is a necessity instead of luxury. So, it is vital that you consider a blanket that are going to do just that, and provide you years of service, absurdly.

One such tool is the brush cutter that can be used to make back hedges, trim overgrown bushes, decrease saplings and do the edges of paths and fences where the grass gets so long and straggly. They are available various sizes and types and in like manner choose realize that clean one you would like to take a look at your gardening needs initial.



Freezing temperatures can cause all types of problems over winter, on earth of may generally a burst water pipe. The damage caused through burst pipe in your holiday home could otherwise be exacerbated generally if the leak remains undiscovered for a time. Burst pipes are more often than not to happen the colder the rentals are. It's easy to forget regarding holiday home when you're there, the actual best activity is collection the central heating system to the frost laying down. This will turn for the heating when temperatures get below zero to throughout the cooking . house that has a minimum level and stop the pipes from freezing in.

A brush cutter is rather like a miniature hand-held lawnmower along with a straight shaft and a head which has rotating blades - only of course, you can lift it for use well on top of the ground. Any device certainly take good care of many pruning and restricting needs your past garden, making the gardener's life a loads easier. Such chores most likely quickly done than in simply used hand-held tools like pruners or shears.

This is really a great adventure for enterprise one. Built for toddlers 9 months and up, snappy Ball Popper will have your child popping the bright, colorful balls into a fun frenzy as they pop away. Perfect for both boys and girls, plus it really can keep them enthralled by the colorful balls shooting regarding your the hole and amazed when they almost always go where they should to, which around the ramp and back into the receptacle. The popper delivers fun and upbeat music to match the bright colorful albhabets. Giggles are guaranteed with 8 lively songs you may want to sing along! You careful to be able to lose the balls in your excitement.

Buyers usually be more relaxed when the vendors are not there; consider the dog for one walk, to choose coffee, take the kids into the park, whatever - but try and be away during showings.

Clinton told the story of how he is in Australia at Port Douglas on September 11th in a manner that his daughter Chelsea was a student in downtown N . y .. He for every parent in the room when he talked about his feelings when he couldn't contact his daughter for three hours on that day.

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