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{{Semireg dual polyhedra db|Semireg dual polyhedron stat table|dtC}}
Your family's lifestyle will vary dramatically with the addition of a patio or deck. You will that a rightly planned outdoor living area can go ahead and take pressure off interior spaces by providing alternative spots for cooking, eating and relaxing.<br><br>
In [[geometry]], a '''triakis octahedron''' is an [[Archimedean solid|Archimedean dual]] solid, or a [[Catalan solid]]. Its dual is the [[truncated cube]].


It can be seen as an [[octahedron]] with [[triangular pyramid]]s added to each face; that is, it is the [[Kleetope]] of the octahedron. It is also sometimes called a ''trisoctahedron'', or, more fully, ''trigonal trisoctahedron''. Both names reflect the fact that it has three triangular faces for every face of an octahedron. The ''tetragonal trisoctahedron'' is another name for the [[deltoidal icositetrahedron]], a different polyhedron with three quadrilateral faces for every face of an octahedron.
<br><br>Look for ways individual can be useful---Maybe the actual can't mow the lawn or trim the hedges, but sit him down in a chair with a task that isn't that laborious. For example, make sure he can fold paper bags or sort written documents. Encourage them think about part in church outreach, such as singing for a nursing residential. It's so in order to let them know they're still useful and a blessing to others.<br><br>The trees in a garden can even be bordered any low outlet. The stone wall can also be used as a sitting area. It would be a perfect spot to take a seat under cooler areas of your tree with a great book.<br><br>The meat complex includes Live Cattle, Feeder Cattle, Lean Hogs, and the ever-popular Pork Bellies. The name, "Pork Bellies" may seem funny, however it's actually frozen bacon. The meat complex has a lot of similarities amongst its men and women. However, at times their differences and situations can be extremely different.<br><br>Even this implies have a green thumb, you can still dress up your property with flowers. Just go to the nearest nursery and acquire fully mature plants which usually ready to bloom. A little watering 1 week can keep these flowers up to par. It is important to get plants that have previously started blooming, and plant them close together for every collective trauma. One or two pots of blooming plants by the front step or porch can add immediate charm to dwelling.<br><br>Lavender is often a great insect and moth repellent. Involving past it was used as being a 'strewing herb' in hospitals and homes to disinfect and clear the air. Dried lavender blossoms make excellent potpourri and could be tied up in cotton fabric prior to being tucked into drawers or linen closets. The branches are also highly fragrant and could be layered into woodpiles assistance out insects.<br><br>Lets start with the outdoor livable space. The lie of the land determines how your patio will take shape. Generally if the ground slopes heavily from your house, you may wish to consider building a wooden boat. These are often efficient alternatives for such types of situations. If your lucky enough to possess a more level plot, you the option of building your patio from cast concrete or packet. Basically any building product will function.<br><br>Trees are the most in danger of drought conditions and you are going to spot problems until its too late so give them a few regular buckets of bath water 1 week. And if the council has planted a tree in your street throughout the last year then get out and give an extra boost using a bucket too!<br><br>If you have any kind of inquiries concerning where and ways to use [http://www.hedgingplants.com/ hedging], you could call us at the website.
 
This convex polyhedron is topologically similar to the concave [[stellated octahedron]]. They have the same face connectivity, but the vertices are in different relative distances from the center.
 
It is also called the [[small triakis octahedron]], so as to differentiate it from the [[great triakis octahedron]], the dual of the [[stellated truncated hexahedron]].
 
If its shorter edges have length 1, its surface area and volume are:
:<math>A=3\sqrt{7+4\sqrt{2}}</math>  
:<math>V=\frac{1}{2}(3+2\sqrt{2}).</math>
 
==Orthogonal projections==
The ''triakis octahedron'' and its dual [[truncated cube]] have five special [[orthogonal projection]]s, centered, on a vertex, on two types of edges, and two types of faces: triangles, and octagons. The last two correspond to the B<sub>2</sub> and A<sub>2</sub> [[Coxeter plane]]s.
{|class=wikitable width=640
|+ Orthogonal projections
|-
!Centered by
!Vertex
!Edge<br>3-8
!Edge<br>8-8
!Face<br>Octagon
!Face<br>Triangle
|-
!Truncated<BR>cube
|[[File:Cube t01 v.png|100px]]
|[[File:Cube t01 e38.png|100px]]
|[[File:Cube t01 e88.png|100px]]
|[[File:3-cube t01_B2.svg|100px]]
|[[File:3-cube t01.svg|100px]]
|-
!Triakis<BR>octahedron
|[[File:Dual truncated cube t01 v.png|100px]]
|[[File:Dual truncated cube t01 e8.png|100px]]
|[[File:Dual truncated cube t01 e88.png|100px]]
|[[File:Dual truncated cube t01_B2.png|100px]]
|[[File:Dual truncated cube t01.png|100px]]
|- align=center
!Projective<BR>symmetry
|[2]
|[2]
|[2]
|[4]
|[6]
|}
 
==Cultural references==
*A triakis octahedron is a vital element in the plot of cult author [[Hugh Cook (science fiction author)|Hugh Cook]]'s novel [[Chronicles of an Age of Darkness#The Wishstone and the Wonderworkers|The Wishstone and the Wonderworkers]].
 
== Related polyhedra ==
The triakis octahedron is one of a family of duals to the uniform polyhedra related to the cube and regular octahedron.
 
{{Octahedral truncations}}
 
The triakis octahedron 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}}
 
The triakis octahedron is also a part of a sequence of polyhedra and tilings, extending into the hyperbolic plane. These [[face-transitive]] figures have (*n42) reflectional [[Orbifold notation|symmetry]].
{{Truncated figure4 table}}
 
==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 17, Triakisoctahedron)
*''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 octahedron)
 
==External links==
*{{Mathworld2 |urlname=SmallTriakisOctahedron |title=Triakis octahedron |urlname2=CatalanSolid |title2=Catalan solid}}
*[http://polyhedra.org/poly/show/34/triakis_octahedron Triakis Octahedron] – Interactive Polyhedron Model
*[http://www.georgehart.com/virtual-polyhedra/vp.html Virtual Reality Polyhedra] www.georgehart.com: The Encyclopedia of Polyhedra
**[[VRML]] [http://www.georgehart.com/virtual-polyhedra/vrml/triakisoctahedron.wrl model]
**[http://www.georgehart.com/virtual-polyhedra/conway_notation.html Conway Notation for Polyhedra] Try: "dtC"
 
{{Polyhedron navigator}}
{{Polyhedron-stub}}
 
[[Category:Catalan solids]]

Latest revision as of 06:45, 4 January 2015

Your family's lifestyle will vary dramatically with the addition of a patio or deck. You will that a rightly planned outdoor living area can go ahead and take pressure off interior spaces by providing alternative spots for cooking, eating and relaxing.



Look for ways individual can be useful---Maybe the actual can't mow the lawn or trim the hedges, but sit him down in a chair with a task that isn't that laborious. For example, make sure he can fold paper bags or sort written documents. Encourage them think about part in church outreach, such as singing for a nursing residential. It's so in order to let them know they're still useful and a blessing to others.

The trees in a garden can even be bordered any low outlet. The stone wall can also be used as a sitting area. It would be a perfect spot to take a seat under cooler areas of your tree with a great book.

The meat complex includes Live Cattle, Feeder Cattle, Lean Hogs, and the ever-popular Pork Bellies. The name, "Pork Bellies" may seem funny, however it's actually frozen bacon. The meat complex has a lot of similarities amongst its men and women. However, at times their differences and situations can be extremely different.

Even this implies have a green thumb, you can still dress up your property with flowers. Just go to the nearest nursery and acquire fully mature plants which usually ready to bloom. A little watering 1 week can keep these flowers up to par. It is important to get plants that have previously started blooming, and plant them close together for every collective trauma. One or two pots of blooming plants by the front step or porch can add immediate charm to dwelling.

Lavender is often a great insect and moth repellent. Involving past it was used as being a 'strewing herb' in hospitals and homes to disinfect and clear the air. Dried lavender blossoms make excellent potpourri and could be tied up in cotton fabric prior to being tucked into drawers or linen closets. The branches are also highly fragrant and could be layered into woodpiles assistance out insects.

Lets start with the outdoor livable space. The lie of the land determines how your patio will take shape. Generally if the ground slopes heavily from your house, you may wish to consider building a wooden boat. These are often efficient alternatives for such types of situations. If your lucky enough to possess a more level plot, you the option of building your patio from cast concrete or packet. Basically any building product will function.

Trees are the most in danger of drought conditions and you are going to spot problems until its too late so give them a few regular buckets of bath water 1 week. And if the council has planted a tree in your street throughout the last year then get out and give an extra boost using a bucket too!

If you have any kind of inquiries concerning where and ways to use hedging, you could call us at the website.

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