File:Academ Elevation Cube in its dual.svg
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Summary[edit]
| Description |
English: Perspective of a cube in a regular octahedron by orthographic projection onto a plane. The vertices of the cube are the centers of the faces of the octahedron. In this image and in the elevation view of this other one, the view of the octahedron is the same, and some notations are the same. T and V are the centers of ABC and HLU, the horizontal faces of the octahedron. The cube and the octahedron have the same center S: the midpoint of the vertical diagonal [VT ] of the cube, and the center of the inscribed sphere and circumscribed sphere of the octahedron. The outline of the cube is VKTE, a diagonal cross section of the cube, its rectangular intersection with the vertical plane (ATH ). The view does not distort VKTE because its plane is parallel to the projection plane. The edge length of the octahedron is a or BU. The altitude of a equilateral face of the octahedron is t. The difference in height between the endpoints of any edge of the cube is h. The distance between two opposite faces of the octahedron is VT or 3 h. Some relations between the lengths are included in the image.
Français : Perspective d’un cube dans un octaèdre régulier par projection orthogonale sur un plan. Les sommets du cube sont les centres des faces de l’octaèdre. Dans cette image et dans la vue en élévation de cette autre, la vue de l’octaèdre est la même, et certaines notations sont les mêmes. T et V sont les centres de ABC et HLU, les faces horizontales de l’octaèdre. Le cube et l’octaèdre ont le même centre S : le milieu de la diagonale verticale [VT ] du cube, et le centre des sphères inscrite et circonscrite à l’octaèdre. Le contour du cube est VKTE, une section diagonale du cube, son intersection rectangulaire avec le plan vertical (ATH ). La perspective ne déforme pas VKTE parce que son plan est parallèle au plan de projection. La longueur d’une arête de l’octaèdre est a ou BU. La hauteur d’une face équilatérale de l’octaèdre est t. La différence de hauteur entre les extrêmités de n’importe quelle arête du cube est h. La distance entre deux faces opposées de l’octaèdre est VT ou 3 h. Des relations entre des longueurs sont inscrites dans l’image. |
| 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
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 08:35, 28 September 2010 | | 720 × 720 (4 KB) | Baelde (talk | contribs) | mieux disposer les informations, supprimer le pointillé vertical de la diagonale du cube, nommer autrement certains points |
| 06:19, 19 March 2010 |  | 720 × 630 (3 KB) | Baelde (talk | contribs) | {{Information |Description={{en|1=Elevation view of a cube in its dual: a regular octahedron named ABCKMN. The equilateral triangles ABC and KMN are horizontal. The inscribed sphere and the circumscribed sphere to ABCKMN have the same center� |
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