en>中川宏: /* Related polyhedral and Honeycombs */

2014-11-11T06:42:19Z

Related polyhedral and Honeycombs

en>Frietjes: copyedit

2013-09-12T18:03:45Z

copyedit

← Older revision		Revision as of 20:03, 12 September 2013
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	~~The title of~~ the ~~writer~~ is ~~Nestor~~. ~~My job is~~ a ~~manufacturing~~ and ~~distribution officer~~ and I'~~m performing pretty good financially~~. ~~Playing crochet~~ is a ~~factor that I~~'~~m totally addicted to~~. ~~Delaware~~ is ~~our birth place~~.<br><br>~~Visit my web page~~: [http://www.~~Planetplayschool~~.com/~~ActivityFeed~~/~~MyProfile~~/~~tabid~~/61/~~UserId/415/Default~~.~~aspx extended auto warranty companies~~]		{{Infobox polyhedron
			\|image=gyrobifastigium.png
			\|type=[[Johnson solid\|Johnson]]<br>[[gyroelongated pentagonal rotunda\|''J''<sub>25</sub>]] -''' J<sub>26</sub>''' - [[triangular orthobicupola\|J<sub>27</sub>]]
			\|faces=4 [[triangle]]s<br>4 [[Square (geometry)\|square]]s
			\|edges=14
			\|vertices=8
			\|symmetry=''D''<sub>2d</sub>
			\|vertex_config=4(3.4<sup>2</sup>)<br>4(3.4.3.4)
			\|dual=-
			\|properties=[[convex set\|convex]], [[honeycomb]]
			\|net=Johnson solid 26 net.png
			}}

			In [[geometry]], the '''gyrobifastigium''' is the 26th [[Johnson solid]] (''J''<sub>26</sub>). It can be constructed by joining two face-regular [[triangular prism]]s along corresponding square faces, giving a quarter-turn to one prism.

			{{Johnson solid}}

			The name comes from the Latin ''fastigium'', meaning a sloping roof.<ref>[http://penelope.uchicago.edu/Thayer/E/Roman/Texts/secondary/SMIGRA*/Fastigium.html William Smith, D.C.L., LL.D.: A Dictionary of Greek and Roman Antiquities, John Murray, London, 1875]</ref> In the standard naming convention of the Johnson solids, ''bi-'' means two solids connected at their bases, and ''gyro-'' means the two halves are twisted with respect to each other.

			The gyrobifastigium's place in the list of Johnson solids, immediately before the [[bicupola (geometry)\|bicupolas]], is explained by viewing it as a ''digonal gyrobicupola''. Just as the other regular cupolas have an alternating sequence of squares and triangles surrounding a single polygon at the top ([[triangular cupola\|triangle]], [[square cupola\|square]] or [[pentagonal cupola\|pentagon]]), each half of the gyrobifastigium consists of just alternating squares and triangles, connected at the top only by a ridge.

			The gyrobifastigium is one of five convex polyhedra with regular faces capable of [[Space-filling polyhedron\|space-filling]] (the others being the [[cube]], [[truncated octahedron]], [[triangular prism\|triangular]] and [[hexagonal prism]]) and it is the only Johnson solid capable of doing so.<ref>{{mathworld \| urlname = Space-FillingPolyhedron \| title = Space-Filling Polyhedron}}</ref><ref>{{mathworld \| urlname = JohnsonSolid \| title = Johnson solid}}</ref><ref>{{mathworld \| urlname = Gyrobifastigium \| title = Gyrobifastigium}}</ref> The 92 Johnson solids were named and described by [[Norman Johnson (mathematician)\|Norman Johnson]] in 1966.

			==Formulae==
			The following [[formula]]e for [[volume]] and [[surface area]] can be used if all [[face (geometry)\|faces]] are [[regular polygon\|regular]], with edge length ''a'':<ref>[[Stephen Wolfram]], "[http://www.wolframalpha.com/input/?i=gyrobifastigium Gyrobifastigium]" from [[Wolfram Alpha]]. Retrieved July 21, 2010.</ref>

			:<math>V=(\frac{\sqrt{3}}{2})a^3\approx0.866025...a^3</math>

			:<math>A=(4+\sqrt{3})a^2\approx5.73205...a^2</math>

			== Dual polyhedron ==

			The dual of the gyrobifastigium has 8 faces: 4 [[isoceles triangle]]s, and 4 [[parallelogram]]s.
			{\| class=wikitable width=320
			\|- valign=top
			!Dual gyrobifastigium
			<!--!Net of dual-->
			\|- valign=top
			\|[[File:Dual gyrobifastigium.png\|160px]]
			<!--\|[[File:Dual gyrobifastigium net.png\|160px]]-->
			\|}

			==References==
			{{reflist}}

			[[Category:Johnson solids]]
			[[Category:Space-filling polyhedra]]

en>Tamfang at 08:02, 6 June 2012

2012-06-06T08:02:19Z

New page

The title of the writer is Nestor. My job is a manufacturing and distribution officer and I'm performing pretty good financially. Playing crochet is a factor that I'm totally addicted to. Delaware is our birth place.<br><br>Visit my web page: [http://www.Planetplayschool.com/ActivityFeed/MyProfile/tabid/61/UserId/415/Default.aspx extended auto warranty companies]

Elongated triangular pyramid - Revision history

en>中川 宏: /* Related polyhedral and Honeycombs */

en>Frietjes: copyedit

en>Tamfang at 08:02, 6 June 2012

en>中川宏: /* Related polyhedral and Honeycombs */