Vibration of plates: Difference between revisions

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Compound moves! But you probably already know just that throughout the countless other articles which ensures you keep repeating this unique. So I'm going to permit you associated with secret. The secret about the training portion is in the quantity of sets, connected with reps, weight and rest between positions. Generally, when bulking up, you should aim to kick or punch a higher weight, with lower officials. This combined with compound exercises will boost your testosterone production levels sky-high resulting fit results. Target your chest, shoulders and upper back muscles with exercises for maximum V-shape effects!<br><br>Yes! Like fat in any other area, belly fat can also be reduced. Obesity is not an overnight condition and it cannot be lost in a night either. Should certainly control more effective . on a regular basis. Do not go for crash eating habits as they harmful for your body publicize your body fatter after they are not followed once more.<br><br>The best mass building exercises are, squats, deadlifts, bench press and pull-ups. If you probably nothing else, except for these exercises, you'll be 90 percent of the way there.<br><br>The first  [http://musclebuildingdiets.net/ Muscle Building Diet] step you have to do is find a weight training program. The second step a person take is eat the best foods and also the correct associated with those healthy foods. Diet and nutrition is very important, however want to debate this powerful method that relates to all of your weightlifting prepare.<br><br>The best foods for [http://musclebuildingdiets.net/ Muscle Building Diet Reviews] Building are chicken, tuna, whole egg, low fat milk and whey protein. Eating these types of food be sure that you're getting adequate amount of Muscle Building protein and also maximize your gains.<br><br>Although could teach the beginning necessarily the best way build  [http://musclebuildingdiets.net/ Muscle Building Diet Reviews] muscle, it a good absolute must when referring to the normal process. That you simply to know where you began and an individual are progressing, tracking your progress on a consistent basis assistance you.<br><br>The ditto goes that diet also. There are different ways to consume just and there is different to be able to exercise. People who need to lose weight naturally would to not have the same diet plan as those who need to achieve weight.<br><br>In most activities, better you do something, superior the results you get. In gym routines, reality isn't faithful. You do not build muscle while an individual might be exercising; you build them while happen to be resting. Exercising is only once stimulate the growth, next you need we are able to body relaxation it requires to actually build muscle mass.
|- align=center valign=top
|[[File:5-cube t0.svg|160px]]<BR><small>[[5-cube]]</small><BR>{{CDD|node_1|4|node|3|node|3|node|3|node}}
|[[File:5-cube t04.svg|160px]]<BR><small>Stericated 5-cube</small><BR>{{CDD|node_1|4|node|3|node|3|node|3|node_1}}
|[[File:5-cube t014.svg|160px]]<BR><small>Steritruncated 5-cube</small><BR>{{CDD|node_1|4|node_1|3|node|3|node|3|node_1}}
|- align=center valign=top
|[[File:5-cube t024.svg|160px]]<BR><small>Stericantellated 5-cube</small><BR>{{CDD|node_1|4|node|3|node_1|3|node|3|node_1}}
|[[File:5-cube t034.svg|160px]]<BR><small>[[Steritruncated 5-orthoplex]]</small><BR>{{CDD|node_1|4|node|3|node|3|node_1|3|node_1}}
|[[File:5-cube t0124.svg|160px]]<BR><small>Stericantitruncated 5-cube</small><BR>{{CDD|node_1|4|node_1|3|node_1|3|node|3|node_1}}
|- align=center valign=top
|[[File:5-cube t0134.svg|160px]]<BR><small>Steriruncitruncated 5-cube</small><BR>{{CDD|node_1|4|node_1|3|node|3|node_1|3|node_1}}
|[[File:5-cube t0234.svg|160px]]<BR><small>[[Stericantitruncated 5-orthoplex]]</small><BR>{{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1}}
|[[File:5-cube t01234.svg|160px]]<BR>[[Omnitruncated 5-cube]]<BR>{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node_1}}
|-
!colspan=3|[[Orthogonal projection]]s in BC<sub>5</sub> [[Coxeter plane]]
|}
In [[Five-dimensional space|five-dimensional]] [[geometry]], a '''stericated 5-cube''' is a convex [[uniform 5-polytope]] with fourth-order [[Truncation (geometry)|truncations]] ([[sterication]]) of the regular [[5-cube]].
 
There are eight degrees of sterication for the 5-cube, including permutations of runcination, cantellation, and truncation. The simple stericated 5-cube is also called an '''expanded 5-cube''', with the first and last nodes ringed, for being [[constructible polygon|constructible]] by an [[Expansion (geometry)|expansion]] operation applied to the regular 5-cube. The highest form, the '''steriruncicantitruncated 5-cube''', is more simply called an [[#Omnitruncated 5-cube|omnitruncated 5-cube]] with all of the nodes ringed.
 
== Stericated 5-cube ==
{| class="wikitable" align="right" style="margin-left:10px" width="250"
|-
|bgcolor=#e7dcc3 align=center colspan=3|'''Stericated 5-cube'''
|-
|bgcolor=#e7dcc3|Type
|colspan=2|[[Uniform 5-polytope]]
|-
|bgcolor=#e7dcc3|[[Schläfli symbol]]
|colspan=2| 2r2r{4,3,3,3}
|-
|bgcolor=#e7dcc3|[[Coxeter-Dynkin diagram]]
|colspan=2|{{CDD||node_1|4|node||3|node|3|node|3|node_1}}<BR>{{CDD|node|split1|nodes|3a4b|nodes_11}}
|-
|bgcolor=#e7dcc3|4-faces
|242
|-
|bgcolor=#e7dcc3|Cells
|800
|-
|bgcolor=#e7dcc3|Faces
|1040
|-
|bgcolor=#e7dcc3|Edges
|640
|-
|bgcolor=#e7dcc3|Vertices
|160
|-
|bgcolor=#e7dcc3|[[Vertex figure]]
|colspan=2|[[File:Stericated penteract verf.png|80px]]
|-
|bgcolor=#e7dcc3|[[Coxeter group]]
|colspan=2| BC<sub>5</sub> [4,3,3,3]
|-
|bgcolor=#e7dcc3|Properties
|colspan=2|[[Convex polytope|convex]]
|}
 
=== Alternate names ===
* Stericated penteract / Stericated 5-orthoplex / Stericated pentacross
* Expanded penteract / Expanded 5-orthoplex / Expanded pentacross
* Small cellated penteract (Acronym: scan) (Jonathan Bowers)<ref>Klitzing, (x3o3o3o4x - scan)</ref>
 
=== Coordinates ===
The [[Cartesian coordinate]]s of the vertices of a ''stericated 5-cube'' having edge length&nbsp;2 are all permutations of:
 
:<math>\left(\pm1,\ \pm1,\ \pm1,\ \pm1,\ \pm(1+\sqrt{2})\right)</math>
 
=== Images ===
The stericated 5-cube is constructed by a [[sterication]] operation applied to the 5-cube.
 
{{5-cube Coxeter plane graphs|t04|150}}
 
==Steritruncated 5-cube==
{| class="wikitable" align="right" style="margin-left:10px" width="250"
!bgcolor=#e7dcc3 colspan=2|Steritruncated 5-cube
|-
|bgcolor=#e7dcc3|Type||[[uniform polyteron]]
|-
|bgcolor=#e7dcc3|[[Schläfli symbol]]|| t<sub>0,1,4</sub>{4,3,3,3}
|-
|bgcolor=#e7dcc3|[[Coxeter-Dynkin diagram]]s||{{CDD|node_1|4|node_1|3|node|3|node|3|node_1}}
|-
|bgcolor=#e7dcc3|4-faces||242
|-
|bgcolor=#e7dcc3|Cells||1600
|-
|bgcolor=#e7dcc3|Faces||2960
|-
|bgcolor=#e7dcc3|Edges||2240
|-
|bgcolor=#e7dcc3|Vertices||640
|-
|bgcolor=#e7dcc3|[[Vertex figure]]||[[File:Steritruncated 5-cube verf.png|80px]]
|-
|bgcolor=#e7dcc3|[[Coxeter group]]s||BC<sub>5</sub>, [3,3,3,4]
|-
|bgcolor=#e7dcc3|Properties||[[Convex polytope|convex]]
|}
 
===Alternate names===
* Steritruncated penteract
* Prismatotruncated penteract (Acronym: capt) (Jonathan Bowers)<ref>Klitzing, (x3o3o3x4x - capt)</ref>
 
===Construction and coordinates===
 
The [[Cartesian coordinate]]s of the vertices of a ''steritruncated 5-cube'' having edge length&nbsp;2 are all permutations of:
 
:<math>\left(\pm1,\ \pm(1+\sqrt{2}),\ \pm(1+\sqrt{2}),\ \pm(1+\sqrt{2}),\ \pm(1+2\sqrt{2})\right)</math>
 
=== Images ===
 
{{5-cube Coxeter plane graphs|t014|150}}
 
==Stericantellated 5-cube==
{| class="wikitable" align="right" style="margin-left:10px" width="250"
|-
|bgcolor=#e7dcc3 align=center colspan=3|'''Stericantellated 5-cube'''
|-
|bgcolor=#e7dcc3|Type
|colspan=2|[[Uniform 5-polytope]]
|-
|bgcolor=#e7dcc3|[[Schläfli symbol]]
|colspan=2| 2r2r{4,3,3,3}
|-
|bgcolor=#e7dcc3|[[Coxeter-Dynkin diagram]]
|colspan=2|{{CDD||node_1|4|node|3|node_1|3|node|3|node_1}}<BR>{{CDD|node_1|split1|nodes|3a4b|nodes_11}}
|-
|bgcolor=#e7dcc3|4-faces||242
|-
|bgcolor=#e7dcc3|Cells||2080
|-
|bgcolor=#e7dcc3|Faces||4720
|-
|bgcolor=#e7dcc3|Edges||3840
|-
|bgcolor=#e7dcc3|Vertices||960
|-
|bgcolor=#e7dcc3|[[Vertex figure]]
|colspan=2|[[File:Stericantellated 5-cube verf.png|80px]]
|-
|bgcolor=#e7dcc3|[[Coxeter group]]
|colspan=2| BC<sub>5</sub> [4,3,3,3]
|-
|bgcolor=#e7dcc3|Properties
|colspan=2|[[Convex polytope|convex]]
|}
 
=== Alternate names ===
* Stericantellated penteract
* Stericantellated 5-orthoplex, stericantellated pentacross
* Cellirhombated penteractitriacontiditeron (Acronym: carnit) (Jonathan Bowers)<ref>Klitzing, (x3o3x3o4x - carnit)</ref>
 
=== Coordinates ===
The [[Cartesian coordinate]]s of the vertices of a ''stericantellated 5-cube'' having edge length&nbsp;2 are all permutations of:
 
:<math>\left(\pm1,\ \pm1,\ \pm1,\ \pm(1+\sqrt{2}),\ \pm(1+2\sqrt{2})\right)</math>
 
=== Images ===
 
{{5-cube Coxeter plane graphs|t024|150}}
 
==Stericantitruncated 5-cube==
{| class="wikitable" align="right" style="margin-left:10px" width="280"
|-
|bgcolor=#e7dcc3 align=center colspan=3|'''Stericantitruncated 5-cube'''
|-
|bgcolor=#e7dcc3|Type
|[[Uniform 5-polytope]]
|-
|bgcolor=#e7dcc3|[[Schläfli symbol]]
|t<sub>0,1,2,4</sub>{4,3,3,3}
|-
|bgcolor=#e7dcc3|[[Coxeter-Dynkin diagram|Coxeter-Dynkin<BR>diagram]]
|{{CDD|node_1|4|node_1|3|node_1|3|node|3|node_1}}
|-
|bgcolor=#e7dcc3|4-faces||242
|-
|bgcolor=#e7dcc3|Cells||2400
|-
|bgcolor=#e7dcc3|Faces||6000
|-
|bgcolor=#e7dcc3|Edges||5760
|-
|bgcolor=#e7dcc3|Vertices||1920
|-
|bgcolor=#e7dcc3|[[Vertex figure]]
|colspan=2|[[File:Stericanitruncated 5-cube verf.png|80px]]
|-
|bgcolor=#e7dcc3|[[Coxeter group]]
|colspan=2| BC<sub>5</sub> [4,3,3,3]
|-
|bgcolor=#e7dcc3|Properties
|[[Convex polytope|convex]], [[isogonal figure|isogonal]]
|}
 
=== Alternate names ===
* Stericantitruncated penteract
* Steriruncicantellated 16-cell / Biruncicantitruncated pentacross
* Celligreatorhombated penteract (cogrin) (Jonathan Bowers)<ref>Klitzing, (x3o3x3x4x - cogrin)</ref>
 
=== Coordinates ===
The [[Cartesian coordinate]]s of the vertices of an stericantitruncated 5-cube having an edge length of&nbsp;2 are given by all permutations of coordinates and sign of:
 
:<math>\left(1,\ 1+\sqrt{2},\ 1+2\sqrt{2},\ 1+2\sqrt{2},\ 1+3\sqrt{2}\right)</math>
 
=== Images ===
{{5-cube Coxeter plane graphs|t013|150}}
 
==Steriruncitruncated 5-cube==
{| class="wikitable" align="right" style="margin-left:10px" width="280"
|-
|bgcolor=#e7dcc3 align=center colspan=3|'''Steriruncitruncated 5-cube'''
|-
|bgcolor=#e7dcc3|Type
|[[Uniform 5-polytope]]
|-
|bgcolor=#e7dcc3|[[Schläfli symbol]]
|2t2r{4,3,3,3}
|-
|bgcolor=#e7dcc3|[[Coxeter-Dynkin diagram|Coxeter-Dynkin<BR>diagram]]
|{{CDD|node_1|4|node_1|3|node|3|node_1|3|node_1}}<BR>{{CDD|node|split1|nodes_11|3a4b|nodes_11}}
|-
|bgcolor=#e7dcc3|4-faces||242
|-
|bgcolor=#e7dcc3|Cells||2160
|-
|bgcolor=#e7dcc3|Faces||5760
|-
|bgcolor=#e7dcc3|Edges||5760
|-
|bgcolor=#e7dcc3|Vertices||1920
|-
|bgcolor=#e7dcc3|[[Vertex figure]]
|colspan=2|[[File:Steriruncitruncated 5-cube verf.png|80px]]
|-
|bgcolor=#e7dcc3|[[Coxeter group]]
|colspan=2| BC<sub>5</sub> [4,3,3,3]
|-
|bgcolor=#e7dcc3|Properties
|[[Convex polytope|convex]], [[isogonal]]
|}
 
=== Alternate names ===
* Steriruncitruncated penteract / Steriruncitruncated 5-orthoplex / Steriruncitruncated pentacross
* Celliprismatotruncated penteractitriacontiditeron  (captint) (Jonathan Bowers)<ref>Klitzing, (x3x3o3x4x - captint)</ref>
 
=== Coordinates ===
The [[Cartesian coordinate]]s of the vertices of an steriruncitruncated penteract having an edge length of&nbsp;2 are given by all permutations of coordinates and sign of:
 
:<math>\left(1,\ 1+\sqrt{2},\ 1+1\sqrt{2},\ 1+2\sqrt{2},\ 1+3\sqrt{2}\right)</math>
 
=== Images ===
{{5-cube Coxeter plane graphs|t0134|150}}
 
==Steritruncated 5-orthoplex==
{| class="wikitable" align="right" style="margin-left:10px" width="250"
!bgcolor=#e7dcc3 colspan=2|Steritruncated 5-orthoplex
|-
|bgcolor=#e7dcc3|Type||[[uniform polyteron]]
|-
|bgcolor=#e7dcc3|[[Schläfli symbol]]|| t<sub>0,1,4</sub>{3,3,3,4}
|-
|bgcolor=#e7dcc3|[[Coxeter-Dynkin diagram]]s||{{CDD|node_1|4|node|3|node|3|node_1|3|node_1}}
|-
|bgcolor=#e7dcc3|4-faces||242
|-
|bgcolor=#e7dcc3|Cells||1520
|-
|bgcolor=#e7dcc3|Faces||2880
|-
|bgcolor=#e7dcc3|Edges||2240
|-
|bgcolor=#e7dcc3|Vertices||640
|-
|bgcolor=#e7dcc3|[[Vertex figure]]||[[File:Steritruncated 5-orthoplex verf.png|80px]]
|-
|bgcolor=#e7dcc3|[[Coxeter group]]||BC<sub>5</sub>, [3,3,3,4]
|-
|bgcolor=#e7dcc3|Properties||[[Convex polytope|convex]]
|}
 
===Alternate names===
* Steritruncated pentacross
* Celliprismated penteract (Acronym: cappin) (Jonathan Bowers)<ref>Klitzing, (x3x3o3o4x - cappin)</ref>
 
=== Coordinates ===
[[Cartesian coordinates]] for the vertices of a steritruncated 5-orthoplex, centered at the origin, are all [[permutation]]s of
:<math>\left(\pm1,\ \pm1,\ \pm1,\ \pm1,\ \pm(1+\sqrt{2})\right)</math>
 
=== Images ===
{{5-cube Coxeter plane graphs|t034|150}}
 
==Stericantitruncated 5-orthoplex==
{| class="wikitable" align="right" style="margin-left:10px" width="280"
|-
|bgcolor=#e7dcc3 align=center colspan=3|'''Stericantitruncated 5-orthoplex'''
|-
|bgcolor=#e7dcc3|Type
|[[Uniform 5-polytope]]
|-
|bgcolor=#e7dcc3|[[Schläfli symbol]]
|t<sub>0,2,3,4</sub>{4,3,3,3}
|-
|bgcolor=#e7dcc3|[[Coxeter-Dynkin diagram|Coxeter-Dynkin<BR>diagram]]
|{{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1}}
|-
|bgcolor=#e7dcc3|4-faces||242
|-
|bgcolor=#e7dcc3|Cells||2320
|-
|bgcolor=#e7dcc3|Faces||5920
|-
|bgcolor=#e7dcc3|Edges||5760
|-
|bgcolor=#e7dcc3|Vertices||1920
|-
|bgcolor=#e7dcc3|[[Vertex figure]]
|colspan=2|[[File:Stericanitruncated 5-orthoplex verf.png|80px]]
|-
|bgcolor=#e7dcc3|[[Coxeter group]]
|colspan=2| BC<sub>5</sub> [4,3,3,3]
|-
|bgcolor=#e7dcc3|Properties
|[[Convex polytope|convex]], [[isogonal]]
|}
 
=== Alternate names ===
* Stericantitruncated pentacross
* Celligreatorhombated pentacross (cogart) (Jonathan Bowers)<ref>Klitzing, (x3x3x3o4x - cogart)</ref>
 
=== Coordinates ===
The [[Cartesian coordinate]]s of the vertices of an stericantitruncated 5-orthoplex having an edge length of&nbsp;2 are given by all permutations of coordinates and sign of:
 
:<math>\left(1,\ 1,\ 1+\sqrt{2},\ 1+2\sqrt{2},\ 1+3\sqrt{2}\right)</math>
 
=== Images ===
{{5-cube Coxeter plane graphs|t0234|150}}
 
==Omnitruncated 5-cube==
{| class="wikitable" align="right" style="margin-left:10px" width="280"
|-
|bgcolor=#e7dcc3 align=center colspan=3|'''Omnitruncated 5-cube'''
|-
|bgcolor=#e7dcc3|Type
|[[Uniform 5-polytope]]
|-
|bgcolor=#e7dcc3|[[Schläfli symbol]]
|tr2r{4,3,3,3}
|-
|bgcolor=#e7dcc3|[[Coxeter-Dynkin diagram|Coxeter-Dynkin<BR>diagram]]
|{{CDD|node_1|4|node_1|3|node_1|3|node_1|3|node_1}}<BR>{{CDD|node_1|split1|nodes_11|3a4b|nodes_11}}
|-
|bgcolor=#e7dcc3|4-faces||242
|-
|bgcolor=#e7dcc3|Cells||2640
|-
|bgcolor=#e7dcc3|Faces||8160
|-
|bgcolor=#e7dcc3|Edges||9600
|-
|bgcolor=#e7dcc3|Vertices||3840
|-
|bgcolor=#e7dcc3|[[Vertex figure]]
|colspan=2|[[File:Omnitruncated 5-cube verf.png|80px]]<BR>irr. {3,3,3}
|-
|bgcolor=#e7dcc3|[[Coxeter group]]
|colspan=2| BC<sub>5</sub> [4,3,3,3]
|-
|bgcolor=#e7dcc3|Properties
|[[Convex polytope|convex]], [[isogonal]]
|}
 
=== Alternate names ===
* Steriruncicantitruncated 5-cube (Full expansion of [[omnitruncation]] for 5-polytopes by Johnson)
* Omnitruncated penteract
* Omnitruncated 16-cell / omnitruncated pentacross
* Great cellated penteractitriacontiditeron (Jonathan Bowers)<ref>Klitzing, (x3x3x3x4x - gacnet)</ref>
 
=== Coordinates ===
The [[Cartesian coordinate]]s of the vertices of an omnitruncated tesseract having an edge length of&nbsp;2 are given by all permutations of coordinates and sign of:
 
:<math>\left(1,\ 1+\sqrt{2},\ 1+2\sqrt{2},\ 1+3\sqrt{2},\ 1+4\sqrt{2}\right)</math>
 
=== Images ===
{{5-cube Coxeter plane graphs|t01234|150}}
 
== Related polytopes ==
This polytope is one of 31 [[Uniform_polyteron#Uniform_polyteron|uniform polytera]] generated from the regular [[5-cube]] or [[5-orthoplex]].
 
{{Penteract family}}
 
==Notes==
{{reflist}}
 
== References ==
* [[Harold Scott MacDonald Coxeter|H.S.M. Coxeter]]:
** H.S.M. Coxeter, ''Regular Polytopes'', 3rd Edition, Dover New York, 1973
** '''Kaleidoscopes: Selected Writings of H.S.M. Coxeter''', editied by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 [http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471010030.html]
*** (Paper 22) H.S.M. Coxeter, ''Regular and Semi Regular Polytopes I'', [Math. Zeit. 46 (1940) 380-407, MR 2,10]
*** (Paper 23) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes II'', [Math. Zeit. 188 (1985) 559-591]
*** (Paper 24) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes III'', [Math. Zeit. 200 (1988) 3-45]
* [[Norman Johnson (mathematician)|Norman Johnson]] ''Uniform Polytopes'', Manuscript (1991)
** N.W. Johnson: ''The Theory of Uniform Polytopes and Honeycombs'', Ph.D.
* {{KlitzingPolytopes|polytera.htm|5D|uniform polytopes (polytera)}} x3o3o3o4x - scan, x3o3o3x4x - capt, x3o3x3o4x - carnit, x3o3x3x4x - cogrin, x3x3o3x4x - captint, x3x3x3x4x - gacnet, x3x3x3o4x - cogart
 
== External links ==
* {{PolyCell | urlname = glossary.html#simplex| title = Glossary for hyperspace}}
* [http://www.polytope.net/hedrondude/topes.htm Polytopes of Various Dimensions], Jonathan Bowers
* [http://tetraspace.alkaline.org/glossary.htm Multi-dimensional Glossary]
 
{{Polytopes}}
 
[[Category:5-polytopes]]

Latest revision as of 00:29, 26 September 2014

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