File:Academ six unfolded faces dodecahedron.svg
Jump to navigation
Jump to search
Size of this PNG preview of this SVG file: 514 × 600 pixels. Other resolutions: 206 × 240 pixels | 411 × 480 pixels | 658 × 768 pixels | 878 × 1,024 pixels | 1,755 × 2,048 pixels | 720 × 840 pixels.
Original file (SVG file, nominally 720 × 840 pixels, file size: 5 KB)
Captions
Captions
Add a one-line explanation of what this file represents
Summary
[edit]| Description |
English: Unfolding of six faces of a platonic dodecahedron, with notations and equalities. KLMNP is the smallest polygon containing the six unfolded faces. RSUVW is the central face. The side length of all the faces is RS or a, their diagonal length is d or φ a, where φ denotes the golden ratio. G is the common center of KLMNP and RSUVW, which are two convex regular pentagons. The symmetry with respect to G transforms KLMNP into ABCEF. So ALCNFKBMEP is a stellated regular decagon with the same center. Its drawing reveals that of a convex regular decagon with the same center. This convex decagon in thick brown line is the outline of the sheet when folded. We can imagine an animated view of the folding, where RSUVW is fixed, and where a movable vertex of the sheet is depicted by K, which moves on the perpendicular bisector of [UV ]. On this straight line H is a vertex of the decagon, it is the point of arrival of K. On the paths of the images of two movable vertices of the sheet, two arrows are pointing to another point of arrival, another vertex of the decagon, the intersection of (CL ), (FK ) and (EV ).
In this image or in this other one, the outline of the dodecahedron is the same in the top view. The distance between two opposite sides of the outline is the real distance between two opposite edges of the solid, equal to MN or φ d. Français : Patron de six faces d’un dodécaèdre de Platon, avec des notations et des égalités. KLMNP est le plus petit polygone contenant les six faces dépliées. RSUVW est la face centrale. Toutes les faces ont des côtés de longueur RS ou a, et des diagonales de longueur d ou φ a, où φ désigne le nombre d’or. G est le centre commun de KLMNP et RSUVW, qui sont deux pentagones réguliers convexes. La symétrie par rapport à G transforme KLMNP en ABCEF. Ainsi ALCNFKBMEP est un décagone régulier étoilé de même centre. Son tracé révèle celui d’un décagone régulier convexe de même centre. Ce décagone convexe en trait brun épais est le contour de la feuille quand elle est pliée. On peut imaginer une vue animée du pliage, où RSUVW est fixe, et où un sommet mobile de la feuille est représenté par K, qui se déplace sur la médiatrice de [UV ]. Sur cette droite H est un sommet du décagone, c’est le point d’arrivée de K. Sur les trajets des images de deux sommets mobiles de la feuille, deux flèches indiquent un autre point d’arrivée, un autre sommet du décagone, l’intersection de (CL ), (FK ) et (EV ). Dans cette image-ci ou dans cette autre, le contour du dodécaèdre est le même dans la vue de dessus. La distance entre deux côtés opposés du contour est la distance réelle entre deux arêtes opposées du solide, égale à MN ou φ d. |
| Date | |
| Source | Own work |
| Author | Yves Baelde |
| SVG development |  This /Baelde was created with a text editor. |
Licensing
[edit]
Arthur Baelde, the copyright holder of this work, hereby publishes it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
Attribution: Arthur Baelde
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 05:39, 30 September 2010 | | 720 × 840 (5 KB) | Baelde (talk | contribs) | more complete information, with two arrows pointing to a point of arrival on the outline of the sheet when folded |
| 07:01, 4 March 2010 |  | 492 × 492 (3 KB) | Baelde (talk | contribs) | sans spécifier Times en CSS : police non recommandée | |
| 15:25, 2 March 2010 |  | 512 × 512 (3 KB) | Baelde (talk | contribs) | To get better PNG images | |
| 10:05, 2 March 2010 |  | 512 × 512 (3 KB) | Baelde (talk | contribs) | {{Information |Description={{en|1=Bilingual SVG file with 'switch' element: systemLanguage "fr" or "en". <br/>The svg root element has no attribute 'width' or 'height', so that the picture fills the whole width or height of the browser's window.<br/>Unfol |
You cannot overwrite this file.
File usage on Commons
There are no pages that use this file.
File usage on other wikis
The following other wikis use this file:
- Usage on fr.wikiversity.org
