File:A periodic tiling by regular hexagons and equilateral triangles.svg

From Wikimedia Commons, the free media repository
Jump to navigation Jump to search

Original file ‎(SVG file, nominally 600 × 600 pixels, file size: 758 bytes)

Captions

Captions

Infinite tiling by regular elements of two different shapes: hexagons and triangles not edge‑to‑edge. Every element adjoins by any side exactly one element of another shape. Rectangular repetitive pattern in SVG code, aspect ratio of 97:168 ≈ 1:√3.

Summary[edit]

Description
English: All tiling elements of same shape are congruent.  The side length of equilateral triangles is three times the one of sides of hexagons.  Every triangle has one side 45° angled in a mathematical coordinate system ( ‑ 45° in SVG).

To study the SVG code of this image,  first open it with a text editor to access its code (Wikipedia gives a list of text editors).  And then type something that tempts you,  save your changed file (Ctrl + S)  and refresh the window (F5) that displays the SVG image.  For example,  you can replace "matrix(1 1 -1 1 9 -2)"  with "translate(9,-2) scale(1.414) rotate(45)",  and see no noticeable change on the new image.  Every triangle will have a vertical side if patternTransform="matrix(1 1 -1 1 9 -2)"  is removed.  Other example,  append the following element 'path' to the 'pattern' as its last child  ( juste avant </pattern>),  and see notably the rectangular repeated pattern coded from M0 0 below:

<path d="m0 47 97-56v112zm0 112l291-168v336z M0 0H388V672H0z"
      opacity=".36" fill="none" stroke="#00f" stroke-width="15"/>

Français :
Tous les éléments du pavage de même forme sont isométriques.  La longueur des côtés des triangles équilatéraux est trois fois celle des côtés des hexagones.  Chaque triangle a un côté incliné à 45° dans un système de coordonnées mathématique ( ‑ 45° en SVG).

Pour étudier le code SVG de cette image,  d’abord l’ouvrir dans un éditeur de texte pour accéder à son code.  Taper ensuite quelque chose qui vous tente,  enregistrer votre fichier modifié (Ctrl + S)  et actualiser la fenêtre (F5) qui affiche l’image SVG.  Par exemple,  vous pourriez remplacer "matrix(1 1 -1 1 9 -2)"  par "translate(9,-2) scale(1.414) rotate(45)",  et ne constater aucun changement notable dans la nouvelle image.  Chaque triangle aura un côté vertical si patternTransform="matrix(1 1 -1 1 9 -2)"  est supprimé.  Autre exemple,  ajouter l’élément 'path' suivant en dernier enfant du 'pattern'  ( juste avant </pattern>),  et voir notamment le motif répété rectangulaire codé ci‑dessous à partir de M0 0 :

<path d="m0 47 97-56v112zm0 112l291-168v336z M0 0H388V672H0z"
      opacity=".36" fill="none" stroke="#00f" stroke-width="15"/>
Date
Source Own work
Author Baelde
Other versions
With  repetitive  patterns
in  dashed  lines
Always  two  different  colours
for tiles sharing a line segment
Always  two  different  colours
for tiles sharing a line segment

Lineless

Lineless
SVG development
InfoField
 
The SVG code is valid.
 
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:
w:en:Creative Commons
attribution share alike
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/TimeThumbnailDimensionsUserComment
current16:20, 27 January 2022Thumbnail for version as of 16:20, 27 January 2022600 × 600 (758 bytes)Arthur Baelde (talk | contribs) lines more visible,  framing a little changed 
09:13, 28 January 2013Thumbnail for version as of 09:13, 28 January 2013600 × 600 (760 bytes)Baelde (talk | contribs)User created page with UploadWizard

You cannot overwrite this file.

File usage on other wikis

The following other wikis use this file:

Metadata

This file contains additional information such as Exif metadata which may have been added by the digital camera, scanner, or software program used to create or digitize it. If the file has been modified from its original state, some details such as the timestamp may not fully reflect those of the original file. The timestamp is only as accurate as the clock in the camera, and it may be completely wrong.

Retrieved from "https://commons.wikimedia.org/w/index.php?title=File:A_periodic_tiling_by_regular_hexagons_and_equilateral_triangles.svg&oldid=778656446"