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| {| class=wikitable align=right width=450
| | One way to help with weight loss is to clean your teeth right after consuming dinner. This tells your system you are completed with food for the night. The minty clean feeling discourages snacking or drinking high calorie fuilds. A minty mouth and greasy potato chips, for example, do not go well together.<br><br>For the sake of convenience the diet foods have worked their magic on us, but I ain't buying it! These foods are non-nourishing, chemical Raspberry Trim Review laden junk, to begin with are even some nutrition stores. The worst culprits would be protein cafes.<br><br>2- Contact a nutritionist or seek help from weight loss expert(s). Try to reach a learner actually lost a few pounds receive tips. Purchasing can constitute great make it easier to.<br><br>Fruits are certainly helpful. Add fruits within your meal. Fruits will never make you fat whatever how much you [http://raspberrytrimdiet.net/ Raspberry Trim Review] eat them. Red berries, oranges, lemon and apple have grown to be good at burning body fat. Do include them in every day meal.<br><br>Dr. Oz, a popular doctor, surgeon, publisher, and well known TV personality gave Raspberry ketone Plus a thumbs along. He has never been fearful to show his feelings towards this revolutionary software.<br><br>As soon as you're fired up, you can start setting [http://raspberrytrimdiet.net/ Raspberry Trim] your goals already. Set a target weight the actual end of your program and point the actual parts anyone really in order to work with regards to. Then set a time full frame on how much time you'll have in order to achieve these actions.<br><br>Further, all fats aren't your attacker. Your body needs some fat sustain joints as well immune system working normally. Choose low fat options, or foods with natural fat, with regard to avocados. Additionally, low fat dairy is a plus for decline. Studies have shown that because they came from drink low fat milk much more weight than people that not, keeping all other food Raspberry Trim intake the the same.<br><br>[http://raspberrytrimdiet.net/ Raspberry Trim Review] Ketones maximizes your energy, races your metabolism, and burns away excessive fats inside you. It fundamentally grants you an edge that means that you can slim down quicker. |
| |- align=center valign=top
| |
| |[[File:5-cube t4.svg|150px]]<BR><small>[[5-orthoplex]]</small><BR>{{CDD|node_1|3|node|3|node|3|node|4|node}}
| |
| |[[File:5-cube t14.svg|150px]]<BR><small>'''Runcinated 5-orthoplex'''</small><BR>{{CDD|node_1|3|node|3|node|3|node_1|4|node}}
| |
| |[[File:5-cube t03.svg|150px]]<BR><small>[[Runcinated 5-cube]]</small><BR>{{CDD|node|3|node_1|3|node|3|node|4|node_1}}
| |
| |- align=center valign=top
| |
| |[[File:5-cube t124.svg|150px]]<BR><small>'''Runcitruncated 5-orthoplex'''</small><BR>{{CDD|node_1|3|node_1|3|node|3|node_1|4|node}}
| |
| |[[File:5-cube t134.svg|150px]]<BR><small>'''Runcicantellated 5-orthoplex'''</small><BR>{{CDD|node_1|3|node|3|node_1|3|node_1|4|node}}
| |
| |[[File:5-cube t1234.svg|150px]]<BR><small>'''Runcicantitruncated 5-orthoplex'''</small><BR>{{CDD|node_1|3|node_1|3|node_1|3|node_1|3|node}}
| |
| |- align=center valign=top
| |
| |[[File:5-cube t013.svg|150px]]<BR><small>[[Runcitruncated 5-cube]]</small><BR>{{CDD|node|3|node_1|3|node|3|node_1|4|node_1}}
| |
| |[[File:5-cube t023.svg|150px]]<BR><small>[[Runcicantellated 5-cube]]</small><BR>{{CDD|node|3|node_1|3|node_1|3|node|4|node_1}}
| |
| |[[File:5-cube t0123.svg|150px]]<BR><small>[[Runcicantitruncated 5-cube]]</small><BR>{{CDD|node|3|node_1|3|node_1|3|node_1|4|node_1}}
| |
| |-
| |
| !colspan=3|[[Orthogonal projection]]s in BC<sub>5</sub> [[Coxeter plane]]
| |
| |}
| |
| In [[Five-dimensional space|five-dimensional]] [[geometry]], a '''runcinated 5-orthoplex''' is a convex [[uniform 5-polytope]] with 3rd order [[Truncation (geometry)|truncation]] ([[runcination]]) of the regular [[5-orthoplex]].
| |
| | |
| There are 8 runcinations of the 5-orthoplex with permutations of truncations, and cantellations. Four are more simply constructed relative to the [[5-cube]].
| |
| | |
| {{TOC left}}
| |
| {{-}}
| |
| | |
| ==Runcinated 5-orthoplex==
| |
| {| class="wikitable" align="right" style="margin-left:10px" width="250"
| |
| |-
| |
| |bgcolor=#e7dcc3 align=center colspan=3|'''Runcinated 5-orthoplex'''
| |
| |-
| |
| |bgcolor=#e7dcc3|Type
| |
| |colspan=2|[[Uniform 5-polytope]]
| |
| |-
| |
| |bgcolor=#e7dcc3|[[Schläfli symbol]]
| |
| |colspan=2| t<sub>0,3</sub>{3,3,3,4}
| |
| |-
| |
| |bgcolor=#e7dcc3|[[Coxeter-Dynkin diagram]]
| |
| |colspan=2|{{CDD||node_1|3|node||3|node|3|node_1|4|node}}<BR>{{CDD||node_1|3|node||3|node|split1|nodes_11}}
| |
| |-
| |
| |bgcolor=#e7dcc3|4-faces
| |
| |162
| |
| |-
| |
| |bgcolor=#e7dcc3|Cells
| |
| |1200
| |
| |-
| |
| |bgcolor=#e7dcc3|Faces
| |
| |2160
| |
| |-
| |
| |bgcolor=#e7dcc3|Edges
| |
| |colspan=2|1440
| |
| |-
| |
| |bgcolor=#e7dcc3|Vertices
| |
| |colspan=2|320
| |
| |-
| |
| |bgcolor=#e7dcc3|[[Vertex figure]]
| |
| |colspan=2|[[File:Runcinated pentacross verf.png|80px]]
| |
| |-
| |
| |bgcolor=#e7dcc3|[[Coxeter group]]
| |
| |colspan=2| BC<sub>5</sub> [4,3,3,3]<BR>D<sub>5</sub> [3<sup>2,1,1</sup>]
| |
| |-
| |
| |bgcolor=#e7dcc3|Properties
| |
| |colspan=2|[[Convex polytope|convex]]
| |
| |}
| |
| | |
| === Alternate names ===
| |
| * Runcinated pentacross
| |
| * Small prismated triacontiditeron (Acronym: spat) (Jonathan Bowers)<ref>Klitzing, (x3o3o3x4o - spat)</ref>
| |
| | |
| === Coordinates ===
| |
| The vertices of the can be made in 5-space, as permutations and sign combinations of: | |
| : (0,1,1,1,2)
| |
| | |
| === Images ===
| |
| {{5-cube Coxeter plane graphs|t14|150}}
| |
| | |
| ==Runcitruncated 5-orthoplex==
| |
| {| class="wikitable" align="right" style="margin-left:10px" width="250"
| |
| !bgcolor=#e7dcc3 colspan=2|Runcitruncated 5-orthoplex
| |
| |-
| |
| |bgcolor=#e7dcc3|Type||[[uniform polyteron]]
| |
| |-
| |
| |bgcolor=#e7dcc3|[[Schläfli symbol]]|| t<sub>0,1,3</sub>{3,3,3,4}<BR>t<sub>0,1,3</sub>{3,3<sup>1,1</sup>}
| |
| |-
| |
| |bgcolor=#e7dcc3|[[Coxeter-Dynkin diagram]]s||{{CDD|node|4|node_1|3|node|3|node_1|3|node_1}}<BR>{{CDD|nodes_11|split2|node|3|node_1|3|node_1}}
| |
| |-
| |
| |bgcolor=#e7dcc3|4-faces||162
| |
| |-
| |
| |bgcolor=#e7dcc3|Cells||1440
| |
| |-
| |
| |bgcolor=#e7dcc3|Faces||3680
| |
| |-
| |
| |bgcolor=#e7dcc3|Edges||3360
| |
| |-
| |
| |bgcolor=#e7dcc3|Vertices||960
| |
| |-
| |
| |bgcolor=#e7dcc3|[[Vertex figure]]||[[File:Runcitruncated 5-orthoplex verf.png|80px]]
| |
| |-
| |
| |bgcolor=#e7dcc3|[[Coxeter group]]s||BC<sub>5</sub>, [3,3,3,4]<BR>D<sub>5</sub>, [3<sup>2,1,1</sup>]
| |
| |-
| |
| |bgcolor=#e7dcc3|Properties||[[Convex polytope|convex]]
| |
| |}
| |
| | |
| === Alternate names===
| |
| * Runcitruncated pentacross
| |
| * Prismatotruncated triacontiditeron (Acronym: pattit) (Jonathan Bowers)<ref>Klitzing, (x3x3o3x4o - pattit)</ref>
| |
| | |
| === Coordinates ===
| |
| [[Cartesian coordinates]] for the vertices of a runcitruncated 5-orthoplex, centered at the origin, are all 80 vertices are sign (4) and coordinate (20) [[permutation]]s of
| |
| : (±3,±2,±1,±1,0) | |
| | |
| === Images ===
| |
| | |
| {{5-cube Coxeter plane graphs|t134|150}}
| |
| | |
| ==Runcicantellated 5-orthoplex==
| |
| {| class="wikitable" align="right" style="margin-left:10px" width="250"
| |
| |-
| |
| |bgcolor=#e7dcc3 align=center colspan=3|'''Runcicantellated 5-orthoplex'''
| |
| |-
| |
| |bgcolor=#e7dcc3|Type
| |
| |colspan=2|[[Uniform 5-polytope]]
| |
| |-
| |
| |bgcolor=#e7dcc3|[[Schläfli symbol]]
| |
| |colspan=2| t<sub>0,2,3</sub>{3,3,3,4}<BR>t<sub>0,2,3</sub>{3,3,3<sup>1,1</sup>}
| |
| |-
| |
| |bgcolor=#e7dcc3|[[Coxeter-Dynkin diagram]]
| |
| |colspan=2|{{CDD||node_1|3|node||3|node_1|3|node_1|4|node}}<BR>{{CDD||node_1|3|node||3|node_1|split1|nodes_11}}
| |
| |-
| |
| |bgcolor=#e7dcc3|4-faces||162
| |
| |-
| |
| |bgcolor=#e7dcc3|Cells||1200
| |
| |-
| |
| |bgcolor=#e7dcc3|Faces||2960
| |
| |-
| |
| |bgcolor=#e7dcc3|Edges||2880
| |
| |-
| |
| |bgcolor=#e7dcc3|Vertices||960
| |
| |-
| |
| |bgcolor=#e7dcc3|[[Vertex figure]]
| |
| |colspan=2|[[File:Runcicantellated 5-orthoplex verf.png|80px]]
| |
| |-
| |
| |bgcolor=#e7dcc3|[[Coxeter group]]
| |
| |colspan=2| BC<sub>5</sub> [4,3,3,3]<BR>D<sub>5</sub> [3<sup>2,1,1</sup>]
| |
| |-
| |
| |bgcolor=#e7dcc3|Properties
| |
| |colspan=2|[[Convex polytope|convex]]
| |
| |}
| |
| | |
| === Alternate names ===
| |
| * Runcicantellated pentacross
| |
| * Prismatorhombated triacontiditeron (Acronym: pirt) (Jonathan Bowers)<ref>Klitzing, (x3o3x3x4o - pirt)</ref>
| |
| | |
| === Coordinates ===
| |
| The vertices of the runcicantellated 5-orthoplex can be made in 5-space, as permutations and sign combinations of:
| |
| : (0,1,2,2,3)
| |
| | |
| === Images ===
| |
| {{5-cube Coxeter plane graphs|t124|150}}
| |
| | |
| ==Runcicantitruncated 5-orthoplex==
| |
| {| class="wikitable" align="right" style="margin-left:10px" width="280"
| |
| |-
| |
| |bgcolor=#e7dcc3 align=center colspan=3|'''Runcicantitruncated 5-orthoplex'''
| |
| |-
| |
| |bgcolor=#e7dcc3|Type
| |
| |[[Uniform 5-polytope]]
| |
| |-
| |
| |bgcolor=#e7dcc3|[[Schläfli symbol]]
| |
| |t<sub>0,1,2,3</sub>{3,3,3,4}
| |
| |-
| |
| |bgcolor=#e7dcc3|[[Coxeter-Dynkin diagram|Coxeter-Dynkin<BR>diagram]]
| |
| |{{CDD|node|4|node_1|3|node_1|3|node_1|3|node_1}}<BR>{{CDD|nodes_11|split2|node_1|3|node_1|3|node_1}}
| |
| |-
| |
| |bgcolor=#e7dcc3|4-faces||162
| |
| |-
| |
| |bgcolor=#e7dcc3|Cells||1440
| |
| |-
| |
| |bgcolor=#e7dcc3|Faces||4160
| |
| |-
| |
| |bgcolor=#e7dcc3|Edges||4800
| |
| |-
| |
| |bgcolor=#e7dcc3|Vertices||1920
| |
| |-
| |
| |bgcolor=#e7dcc3|[[Vertex figure]]
| |
| |colspan=2|[[File:Runcicantitruncated 5-orthoplex verf.png|80px]]<BR>[[Irregular 5-cell]]
| |
| |-
| |
| |bgcolor=#e7dcc3|[[Coxeter group]]s
| |
| |colspan=2| BC<sub>5</sub> [4,3,3,3]<BR>D<sub>5</sub> [3<sup>2,1,1</sup>]
| |
| |-
| |
| |bgcolor=#e7dcc3|Properties
| |
| |[[Convex polytope|convex]], [[isogonal]]
| |
| |}
| |
| | |
| === Alternate names ===
| |
| * Runcicantitruncated pentacross
| |
| * Great prismated triacontiditeron (gippit) (Jonathan Bowers)<ref>Klitzing, (x3x3x3x4o - gippit)</ref>
| |
| | |
| === Coordinates ===
| |
| | |
| The [[Cartesian coordinate]]s of the vertices of an runcicantitruncated tesseract having an edge length of √2 are given by all permutations of coordinates and sign of:
| |
| | |
| :<math>\left(0, 1, 2, 3, 4\right)</math>
| |
| | |
| === Images ===
| |
| {{5-cube Coxeter plane graphs|t123|150}}
| |
| | |
| === Snub 5-demicube ===
| |
| | |
| The '''snub 5-demicube''' defined as an [[Alternation (geometry)|alternation]] of the omnitruncated 5-demicube is not uniform, but it can be given Coxeter diagram {{CDD|nodes_hh|split2|node_h|3|node_h|3|node_h}} or {{CDD|node|4|node_h|3|node_h|3|node_h|3|node_h}} and [[Coxeter notation|symmetry]] [3<sup>2,1,1</sup>]<sup>+</sup> or [4,(3,3,3)<sup>+</sup>], and constructed from 32 [[snub 5-cell]]s, 80 alternated 6-6 [[duoprism]]s, 40 [[icosahedral prism]]s, 10 [[snub 24-cell]]s, and 960 irregular [[tetrahedron]]s filling the gaps at the deleted vertices.
| |
| | |
| == 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)}} x3o3o3x4o - spat, x3x3o3x4o - pattit, x3o3x3x4o - pirt, x3x3x3x4o - gippit
| |
| | |
| == 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://www.polytope.net/hedrondude/truncates5.htm Runcinated uniform polytera] (spid), Jonathan Bowers
| |
| * [http://tetraspace.alkaline.org/glossary.htm Multi-dimensional Glossary]
| |
| | |
| {{Polytopes}}
| |
| | |
| [[Category:5-polytopes]]
| |
One way to help with weight loss is to clean your teeth right after consuming dinner. This tells your system you are completed with food for the night. The minty clean feeling discourages snacking or drinking high calorie fuilds. A minty mouth and greasy potato chips, for example, do not go well together.
For the sake of convenience the diet foods have worked their magic on us, but I ain't buying it! These foods are non-nourishing, chemical Raspberry Trim Review laden junk, to begin with are even some nutrition stores. The worst culprits would be protein cafes.
2- Contact a nutritionist or seek help from weight loss expert(s). Try to reach a learner actually lost a few pounds receive tips. Purchasing can constitute great make it easier to.
Fruits are certainly helpful. Add fruits within your meal. Fruits will never make you fat whatever how much you Raspberry Trim Review eat them. Red berries, oranges, lemon and apple have grown to be good at burning body fat. Do include them in every day meal.
Dr. Oz, a popular doctor, surgeon, publisher, and well known TV personality gave Raspberry ketone Plus a thumbs along. He has never been fearful to show his feelings towards this revolutionary software.
As soon as you're fired up, you can start setting Raspberry Trim your goals already. Set a target weight the actual end of your program and point the actual parts anyone really in order to work with regards to. Then set a time full frame on how much time you'll have in order to achieve these actions.
Further, all fats aren't your attacker. Your body needs some fat sustain joints as well immune system working normally. Choose low fat options, or foods with natural fat, with regard to avocados. Additionally, low fat dairy is a plus for decline. Studies have shown that because they came from drink low fat milk much more weight than people that not, keeping all other food Raspberry Trim intake the the same.
Raspberry Trim Review Ketones maximizes your energy, races your metabolism, and burns away excessive fats inside you. It fundamentally grants you an edge that means that you can slim down quicker.