File:Academviews Platonic dodecahedron.svg
Jump to navigation
Jump to search
Size of this PNG preview of this SVG file: 450 × 600 pixels. Other resolutions: 180 × 240 pixels | 360 × 480 pixels | 576 × 768 pixels | 768 × 1,024 pixels | 1,536 × 2,048 pixels | 720 × 960 pixels.
Original file (SVG file, nominally 720 × 960 pixels, file size: 6 KB)
Captions
Captions
Add a one-line explanation of what this file represents
Summary[edit]
| Description |
English: Elevation view and top view of a platonic dodecahedron, with notations and equalities. The faces of the solid have the same colors in this image and this other one. φ is the golden ratio. The dodecahedron is centrally symmetric, its center is Ω. Its edge length is a, and φ a or d is the diagonal length of its faces. φ d is the distance between two opposite edges.
Two opposite faces are horizontal, RSUVW is the upper face. When seen from above, the common axis of the horizontal faces is depicted like Ω, and the outline of the solid is a convex regular decagon. When the solid rotates one fifth of a turn around this vertical axis, it returns to its initial orientation whatever the sense of rotation. Infinitely many horizontal cross sections are convex regular pentagons, ABCEF and KLMNP are the two largest. Any horizontal cross section that is not pentagonal is a convex decagon, which has the vertices of two congruent regular pentagons with the same center. The axis of EKCUV and the lines (AR ) and (NB ) intersect in T. A homothecy with center T and a ratio strictly between 1 and φ transforms the face in the plane (NBS ) into a pentagonal cross section parallel to (NBS ) and (EKC ). Some cross sections of the solid are squares, some of these squares are drawn in yellow. Each face of the dodecahedron has a yellow diagonal, the twelve yellow segments are the edges of a cube inside the dodecahedron. The center of this cube is Ω. The homothecy with center Ω and ratio φ scales up this cube into another, depicted with thick grey edges. Each face of this second cube contains an edge of the dodecahedron, of which the midpoint is the center of the square face. Two sides of the square are parallel to the edge in the square. An infinite number of cross sections are equilateral triangles. The edges of both of them but an edge of cube are in green. The two triangular sections are perpendicular to (RΩ ). Français : Vue en élévation et vue de dessus d’un dodécaèdre de Platon, avec des notations et des égalités. Les faces du solide ont les mêmes couleurs dans cette image et dans cette autre. φ est le nombre d’or. Le centre Ω du dodécaèdre est son centre de symétrie. La longueur de ses arêtes est a, et φ a ou d est la longueur d’une diagonale d’une face. φ d est la distance entre deux arêtes opposées. Deux faces opposées sont horizontales, RSUVW est la face supérieure. En vue de dessus, l’axe commun des faces horizontales est représenté comme Ω, et le contour du solide est un décagone régulier convexe. Quand le solide tourne d’un cinquième de tour autour de cet axe vertical, il revient à son orientation initiale quel que soit le sens de rotation. Un nombre infini de sections horizontales sont des pentagones réguliers convexes, ABCEF et KLMNP sont les deux plus grands. Toute section horizontale qui n’est pas pentagonale est un décagone convexe, qui a les sommets de deux pentagones réguliers isométriques et concentriques. L’axe de EKCUV et les droites (AR ) et (NB ) se coupent en T. Une homothétie de centre T et de rapport compris entre 1 et φ strictement transforme la face dans le plan (NBS ) en une section pentagonale parallèle à (NBS ) et (EKC ). Certaines sections du solide sont des carrés, certains de ces carrés sont tracés en jaune. Chaque face du dodécaèdre a une diagonale jaune, les douze segments jaunes sont les arêtes d’un cube à l’intérieur du dodécaèdre. Le centre de ce cube est Ω. L’homothétie de centre Ω et de rapport φ agrandit ce cube en un autre, représenté avec des arêtes grises épaisses. Chaque face de ce second cube contient une arête du dodécaèdre, dont le milieu est le centre de la face carrée. Deux côtés du carré sont parallèles à l’arête dans le carré. Un nombre infini de sections sont des triangles équilatéraux. Les côtés de deux d’entre eux sont verts, sauf une arête d’un cube. Les deux sections triangulaires sont perpendiculaires à (RΩ ). |
| Date | 02/03/2010 |
| 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 | 10:19, 7 October 2010 | | 720 × 960 (6 KB) | Baelde (talk | contribs) | Now we see six edges of the dodecahedron on the surface of a cube |
| 06:53, 4 March 2010 |  | 450 × 600 (5 KB) | Baelde (talk | contribs) | et sans élément use | |
| 06:37, 4 March 2010 |  | 512 × 683 (5 KB) | Baelde (talk | contribs) | spécification Times supprimée du CSS : police non recommandée | |
| 14:54, 2 March 2010 |  | 1,536 × 2,048 (5 KB) | Baelde (talk | contribs) | To get a good PNG file 2000px | |
| 14:48, 2 March 2010 |  | 768 × 1,024 (5 KB) | Baelde (talk | contribs) | I try again | |
| 14:40, 2 March 2010 |  | 768 × 1,024 (5 KB) | Baelde (talk | contribs) | With 'width' and 'height' attributes | |
| 10:54, 2 March 2010 |  | 512 × 683 (5 KB) | Baelde (talk | contribs) | Poorly converted to PNG by Commons : switch and use removed | |
| 10:23, 2 March 2010 |  | 512 × 683 (5 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/>Eleva |
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
