File:Academ RegularOctahedronSeenInTheDirectionOfADiagonal RegularCrossSections.svg
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editDescriptionAcadem RegularOctahedronSeenInTheDirectionOfADiagonal RegularCrossSections.svg |
English: Perspective of a regular octahedron by orthographic projection onto a plane parallel to a diagonal square of the solid. No letters to denote the points, but the hexagonal cross sections and the colors of the faces and edges are the same in this image, where notations exist. The same octahedron again is in this other image. The diagonal square with green sides is the outline of the solid, depicted with its true shape. It is easy to imagine the effect of a quarter turn around the diagonal of the solid, which is parallel to the sight direction. Whatever the sense of the rotation, one quarter turn around a diagonal of the octahedron transforms the octahedron into itself, and also preserves a cross section perpendicular to this diagonal.
In front of the solid the altitudes of each face are three yellow lines. The orthocenter of a face is the center of a target, we imagine the two orange circles of the target painted on the face. The projection distorts the four targets and the twelve symbols of right angles at the feet of the altitudes. The projection also distorts a cross section of the solid parallel to two faces: a hexagon with white sides. The three consecutive sides of the hexagon behind the solid are dashed depicted. Each vertex of the hexagon is the midpoint of an edge of the solid. The three diagonal squares and the white hexagon are four cross sections passing through the center of the solid, that are four regular polygons. Français : Perspective d’un octaèdre régulier par projection orthogonale sur un plan parallèle à un carré diagonal du solide. Pas de lettres pour nommer les points, mais la section hexagonale et les couleurs des faces et des arêtes sont les mêmes dans cette image, où des notations existent. Le même octaèdre encore est dans cette autre image. Le carré diagonal aux côtés vert est le contour du solide, représenté avec sa vraie forme. Il est facile d’imaginer l’effet d’un quart de tour autour de la diagonale du solide, qui est parallèle à la direction de la vue. Quel que soit le sens de la rotation, un quart de tour autour d’une diagonale de l’octaèdre transforme l’octaèdre en lui-même, et conserve aussi une section plane perpendiculaire à cette diagonale. Devant le solide les hauteurs de chaque face sont trois traits jaunes. L’orthocentre d’une face est le centre d’une cible, on imagine les deux cercles orangés de la cible peints sur la face. La projection déforme les quatre cibles et les douze symboles d’angles droits aux pieds des hauteurs. La projection déforme aussi une section plane du solide parallèle à deux faces : un hexagone aux côtés blancs. Les trois côtés consécutifs de l’hexagone blanc situés derrière le solide sont représentés en pointillé. Chaque sommet de l’hexagone est le milieu d’une arête du solide. Les trois carrés diagonaux et l’hexagone blanc sont quatre sections passant par le centre du solide, qui sont quatre polygones réguliers. |
Date | |
Source | Own work |
Author | Yves Baelde |
SVG development InfoField | This /Baelde was created with a text editor. |
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current | 11:23, 1 October 2010 | 720 × 720 (2 KB) | Baelde (talk | contribs) | {{Information |Description={{en|1=Perspective of a regular octahedron by orthographic projection onto a plane parallel to a diagonal square of the solid. No letters to denote the points, but the hexagonal cross sections |
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