File:Assorted golden tilings and regular polygons on Platonic dodecahedron.svg
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Summary
[edit]DescriptionAssorted golden tilings and regular polygons on Platonic dodecahedron.svg |
English:
Six faces of Platonic dodecahedron are six tilings, each consisting of divided into:
Every element of any type is called golden triangle because of its length ratio of two edges:
Any similar elements of tiling are congruent. These tilings are contructed edge‑to‑edge, any boundary between two adjacent elements is a full edge of one and the other element, even if this common edge is on an edge of the dodecahedron, when the two adjacent elements are not coplanar. These six tilings draw nine regular polygons in blue or red lines: two decagons and seven pentagons, including a star pentagon with interlaced edges, each laying on one face of the solid, also three regular cross sections of the solid: a yellow equilateral triangle and two congruent hexagons. These hexagons and the star pentagon have the same edge length. The green hexagon is entirely visible, not distorted by the projection. Each of the two hidden edges of the violet hexagon is parallel and congruent to one of its larger edges on the drawing. The projection shrinks every edge of the violet hexagon. Français : Six faces de dodécaèdre de Platon sont six pavages, constitués chacun de répartis en
Tout élément quel que soit son type s’appelle un triangle d’or en raison d’un rapport des longueurs de deux côtés :
N’importe quels éléments de pavage qui sont semblables sont superposables, disons plus savamment qu’ils sont isométriques. Ces pavages sont construits bord à bord, toute frontière entre deux éléments adjacents est un côté complet de l’un et l’autre élément, même si ce côté commun est sur une arête du dodécaèdre, quand les deux éléments adjacents ne sont pas coplanaires. Ces six pavages dessinent neuf polygones réguliers en traits bleus ou rouges : deux décagones et sept pentagones, y compris un pentagone étoilé aux côtés entrelacés, chacun sur une face du solide, ainsi que trois sections régulières du solide : un triangle équilatéral jaune et deux hexagones de même taille. Ces hexagones et le pentagone étoilé ont des côtés égaux, ou de même longueur. L’hexagone vert est entièrement visible, non déformé par la projection. Chacun des deux côtés cachés de l’hexagone violet est parallèle et égal à l’un de ses côtés les plus grands dans le dessin. La projection rapetisse les côtés de l’hexagone violet. |
Date | |
Source | Own work |
Author | Arthur Baelde |
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SVG development InfoField | This /Baelde was created with a text editor. |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 15:21, 4 September 2021 | 600 × 600 (5 KB) | Arthur Baelde (talk | contribs) | more deep color of edges of the solid | |
13:18, 27 August 2021 | 600 × 600 (16 KB) | Arthur Baelde (talk | contribs) | Uploaded own work with UploadWizard |
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