File:Regular hexagon symmetries.svg

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Original file (SVG file, nominally 886 × 766 pixels, file size: 54 KB)

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Description
English: Hexagon symmetries. SVG obtained from PDF generated using LaTeX source code below and manually edited for default rendering size.
Date
Source

Own work, chart sourced from The Symmetries of Things, p.276, Figure 20.5 Types of Hexagons

  • John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, (2008) The Symmetries of Things, ISBN 978-1-56881-220-5 (Chapter 20, Generalized Schaefli symbols, Types of symmetry of a polygon pp.275-278)
Author Krishnavedala
 
W3C-validity not checked.
LaTeX source code
\documentclass[12pt,border=1pt,tikz,class=scrartcl]{standalone}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{lmodern}
\usepackage{mathtools}
 
\usetikzlibrary{shapes,calc,positioning}
 
\begin{document}
\small
\begin{tikzpicture}[very thick,auto,scale=.5]
	\draw [black]
		(-5,1) -- (-4.134,.5) -- (-4.134,-.5) -- (-5,-1) -- (-5.866,-.5) -- (-5.866,.5) -- (-5,1)
		(12,-7) -- (12.866,-7.5) -- (12.866,-8.5) -- (12,-9) -- (11.134,-8.5) -- (11.134,-7.5) -- (12,-7)
		(17,-7) -- (17.866,-7.5) -- (17.866,-8.5) -- (17,-9) -- (16.134,-8.5) -- (16.134,-7.5) -- (17,-7)
		(12,-12) -- (12.866,-12.5) -- (12.866,-13.5) -- (12,-14) -- (11.134,-13.5) -- (11.134,-12.5) -- (12,-12)
	;
	\draw [red]
		(0,6) -- (.866,5.5) -- (.866,4.5) -- (0,4) -- (-.866,4.5) -- (-.866,5.5) -- (0,6)
		(5,1) -- (5.866,.5)	(5.866,-.5) -- (5,-1)	(4.134,-.5) -- (4.134,.5)
		(12.866,-2.5) -- (12.866,-3.5) 	(11.134,-2.5) -- (11.134,-3.5)
		(7.866,-8.5) -- ++(0,1) 	(6.134,-8.5) -- ++(0,1)
		(0,1) -- ++(-.433,-.25)	(.866,.5) -- ++(-.433,.25)	(.866,-.5) -- ++(0,.5)	(0,-1) -- ++(.433,.25)	(-.866,-.5) -- ++(.433,-.25)	(-.866,.5) -- ++(0,-.5)
	;
	\draw [green]
		(-.866,-4.5) -- (0,-4)	(.866,-4.5) -- (.866,-5.5)	(0,-6) -- (-.866,-5.5)
		(6.134,-7.5) -- (7,-7) -- (7.866,-7.5)
	;
	\draw [blue!60]
		(5,1) -- (4.134,.5)	(4.134,-.5) -- (5,-1)	(5.866,-.5) -- (5.866,.5)
		(11.134,-2.5) -- (12,-2) -- (12.866,-2.5)	(11.134,-3.5) -- (12,-4) -- (12.866,-3.5)
		(6.134,-8.5) -- (7,-9) -- (7.866,-8.5)
		(0,1) -- ++(.433,-.25)	(.866,.5) -- ++(0,-.5)	(.866,-.5) -- ++(-.433,-.25)	(0,-1) -- ++(-.433,.25)	(-.866,-.5) -- ++(0,.5)	(-.866,.5) -- ++(.433,.25)
	;
	\draw [purple] (0,-4) -- (.866,-4.5)	(.866,-5.5) -- (0,-6)	(-.866,-5.5) -- ++(0,1)
	;
	\foreach \angle in {0,30,60,...,330} {
		\pgfmathparse{1.3*cos(\angle)} \let\xa\pgfmathresult
		\pgfmathparse{1.3*sin(\angle)} \let\ya\pgfmathresult
		\draw [blue!60,thin]	(0,5) -- ++(\xa,\ya);
	}
	\foreach \angle in {0,60,...,300} {
		\pgfmathparse{1.3*cos(\angle)} \let\xa\pgfmathresult
		\pgfmathparse{1.3*sin(\angle)} \let\ya\pgfmathresult
		\draw [blue!60,thin]	(5,0) -- ++(\xa,\ya);
	}
	\foreach \angle in {30,90,...,330} {
		\pgfmathparse{1.3*cos(\angle)} \let\xa\pgfmathresult
		\pgfmathparse{1.3*sin(\angle)} \let\ya\pgfmathresult
		\draw [blue!60,thin]	(-5,0) -- ++(\xa,\ya);
	}
	\draw [blue!60,thin] (12,-4.3) -- ++(0,2.6)	(10.8,-3) -- ++(2.4,0)
		(7,-9.3) -- ++(0,2.6)	(15.8,-8) -- ++(2.6,0)
	;
	\draw [fill=green!40,draw=none]
		(0,1) circle (.2)	(.866,.5) circle (.2)	(.866,-.5) circle (.2)	(0,-1) circle (.2) (-.866,-.5) circle (.2) (-.866,.5) circle (.2)
		(0,6) circle (.2)	(.866,5.5) circle (.2)	(.866,4.5) circle (.2)	(0,4) circle (.2) (-.866,4.5) circle (.2) (-.866,5.5) circle (.2)
		(5,1) circle (.2)	(5.866,.5) circle (.2)	(5.866,-.5) circle (.2)	(5,-1) circle (.2) (4.134,-.5) circle (.2) (4.134,.5) circle (.2)
		(12,-2) circle (.2)	(12,-4) circle (.2)
		(7,-7) circle (.2)	(7,-9) circle (.2)
	;
	\draw [fill=blue,draw=none]
		(-5,1) circle (.2)		(-5.866,-.5) circle (.2)		(-4.134,-.5) circle (.2)
		(0,-4) circle (.2)		(-.866,-5.5) circle (.2)		(.866,-5.5) circle (.2)
		(12.866,-7.5) circle (.2)	(11.134,-8.5) circle (.2)
		(17,-7) circle (.2)	(17,-9) circle (.2)
		(11.134,-13.5) circle (.2)
	;
	\draw [fill=red,draw=none]
		(-5,-1) circle (.2)	(-5.866,.5) circle (.2)		(-4.134,.5) circle (.2)
		(0,-6) circle (.2)		(-.866,-4.5) circle (.2)		(.866,-4.5) circle (.2)
		(16.134,-8.5) circle (.2) 	(16.134,-7.5) circle (.2)
		(12,-7) circle (.2) 	(12,-9) circle (.2)
		(12,-12) circle (.2)
	;
	\draw [fill=green!40!gray,draw=none]
		(7.866,-8.5) circle (.2)	(6.134,-8.5) circle (.2)
		(12.866,-8.5) circle (.2) 	(11.134,-7.5) circle (.2)
		(17.866,-8.5) circle (.2) 	(17.866,-7.5) circle (.2)
		(11.134,-12.5) circle (.2)
	;
	\draw [fill=orange,draw=none]
		(12.866,-2.5) circle (.2)	(12.866,-3.5) circle (.2)	(11.134,-2.5) circle (.2)	(11.134,-3.5) circle (.2)
		(12.866,-13.5) circle (.2)
	;
	\draw [fill=purple,draw=none] (6.143,-7.5) circle (.2) (7.866,-7.5) circle (.2) (12,-14) circle (.2);
	\draw [fill=pink,draw=none] (12.866,-12.5) circle (.2);
	\draw [purple!40] (0,1.4) -- ++(0,2)	(1,4) -- ++(3,-3)		(-1,4) -- ++(-3,-3)
		(0,-1.4) -- ++(0,-2)	(1,-4) -- ++(3,+3)		(-1,-4) -- ++(-3,+3)
		(12,-4.6) -- ++(0,-2)	(13,-4) -- ++(3,-3)		(11,-4) -- ++(-3,-3)
		(12,-9.4) -- ++(0,-2)	(13,-12) -- ++(3,+3)	(11,-12) -- ++(-3,+3)
	;
	\draw [purple] 
		(2,5) -- ++(9,-7)	(6.5,-.7) -- ++(9,-7)	(1.5,-.5) -- ++(9,-7)	(-3.5,-.5) -- ++(9,-7)	(1,-6) -- ++(9,-7)
	;
	\draw [every node/.style={ellipse,draw,thin,inner sep=.5pt}] 
		node at (-.9,3) {r12}
		node at (-5.5,-1.5) {d6}
		node at (-.7,-1.5) {g6}
		node at (4.5,-1.5) {p6}
		node at (-.7,-6.5) {g3}
		node at (11.4,-4.4) {i4}
		node at (11.3,-9.5) {g2}
		node at (6.3,-9.5) {d2}
		node at (16.5,-9.5) {p2}
		node at (11.3,-14.5) {a1}
	;
	\draw [every node/.style={circle,draw,thin,inner sep=.5pt}] 
		node at (0,0) {6}
		node at (0,-5) {3}
		node at (12,-8) {2}
		node at (12,-13) {1}
	;
	\draw
		node at (.7,3) {[6]}
		node at (-4.1,-1.5) {[3]$_\mathrm{v}$}
		node at (.7,-1.5) {[6]$^+$}
		node at (5.9,-1.5) {[3]$_\mathrm{e}$}
		node at (.7,-6.5) {[3]$^+$}
		node at (12.6,-4.4) {[2]}
		node at (12.7,-9.5) {[2]$^+$}
		node at (7.5,-9.5) {[1]$_\mathrm{v}$}
		node at (17.9,-9.5) {[1]$_\mathrm{e}$}
		node at (13,-14.5) {[1]$^+$}
	;
\end{tikzpicture}
\end{document}

Licensing

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I, the copyright holder of this work, hereby publish it under the following licenses:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
You are free:
  • to share – to copy, distribute and transmit the work
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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.
GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.
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File history

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Date/TimeThumbnailDimensionsUserComment
current20:20, 4 December 2014Thumbnail for version as of 20:20, 4 December 2014886 × 766 (54 KB)Krishnavedala (talk | contribs)manually edited SVG file for increased dimensions
20:11, 4 December 2014Thumbnail for version as of 20:11, 4 December 2014443 × 383 (54 KB)Krishnavedala (talk | contribs)increased font size for clarity
20:01, 4 December 2014Thumbnail for version as of 20:01, 4 December 2014439 × 379 (54 KB)Krishnavedala (talk | contribs)reduced gaps further
19:30, 4 December 2014Thumbnail for version as of 19:30, 4 December 2014318 × 276 (33 KB)Krishnavedala (talk | contribs)reduced spacing between left and right image sets thus increasing resolution
22:56, 3 December 2014Thumbnail for version as of 22:56, 3 December 2014391 × 314 (39 KB)Krishnavedala (talk | contribs)added missing mirror lines and other labels
16:19, 3 December 2014Thumbnail for version as of 16:19, 3 December 2014387 × 313 (35 KB)Krishnavedala (talk | contribs){{Information |Description ={{en|1=Hexagon symmetries}} |Source ={{own}}, chart sourced from ''The Symmetries of Things'', p.276, Figure 20.5 Types of Hexagons * John H. Conway, Heidi Burgiel, Chaim...

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