File:Associahedron K5 back.svg
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Size of this PNG preview of this SVG file: 266 × 235 pixels. Other resolutions: 272 × 240 pixels | 543 × 480 pixels | 869 × 768 pixels | 1,159 × 1,024 pixels | 2,318 × 2,048 pixels.
Original file (SVG file, nominally 266 × 235 pixels, file size: 28 KB)
Captions
Captions
The 3-dimensional associahedron
Summary[edit]
| Description |
English: A polyhedron whose vertices corresponding to bracketings of a product of five factors, with edges corresponding to rebracketings, from (((ab)c)d)e to a(b(c(de))). |
| Date | |
| Source |
Own work First published at File:Associahedron_K5_back.png; updated here for svg |
| Author | Nilesj |
Tikz Source[edit]
\begin{tikzpicture}[x=1.18mm,y=1mm,scale=1.6]
% node numbering is from Tamari's thesis
% parenthesization is reversed
% https://www.math.wustl.edu/~escobar/pdf/Olivetti2015.pdf
\tikzset{every node/.style={scale=.8}}
\tikzset{>=stealth}
\tikzset{mm/.style={execute at begin node=$\displaystyle, execute at end node=$}}
\draw[mm] %objects
(-7.3,-1.6) node (1120) {\cdot} %{((a(bc))d)e}
(7.3,-1.6) node (1210) {\cdot} %{(a((bc)d)))e}
(0,20) node (3010) {a((bc)(de))}
(0,-19) node (1201) {((ab)(cd))e}
(-16,1) node (2011) {((ab)c)(de)}
(16,1) node (2200) {a((b(cd))e)}
(-11.5,12) node (2020) {(a(bc))(de)}
(11.5,12) node (2110) {a(((bc)d)e)}
(-12,-11) node (1111) {(((ab)c)d)e}
(12,-11) node (1300) {(a(b(cd)))e}
(0,15) node (4000) {a(b(c(de)))}
(0,-5) node (2101) {(ab)((cd)e)}
(-5.5,5) node[transform canvas={xshift=2}] (3001) {(ab)(c(de))}
(5.5,5) node[transform canvas={xshift=-2}] (3100) {a(b((cd)e))}
;
\path[->,dashed, color=black!50!white]
(1111) edge (1120)
(1120) edge (1210)
(1210) edge (2110)
%
(1120) edge (2020)
(1210) edge (1300)
;
\path[->]
(2011) edge[shorten >=-1.8] (3001)
(2200) edge[shorten >=-1.8] (3100)
(1201) edge (2101)
(3010) edge (4000)
%
(2101) edge (3001)
(3001) edge (4000)
(2101) edge (3100)
(3100) edge (4000)
;
\path[->] %arrows
(2110) edge (3010)
(2020) edge (3010)
%
(1111) edge (1201)
(1201) edge (1300)
%
(1111) edge (2011)
(2011) edge (2020)
%
(1300) edge (2200)
(2110) edge (2200)
;
\end{tikzpicture}
Licensing[edit]
I, the copyright holder of this work, hereby publish it under the following license:
 
|
This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
| The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
|
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 22:40, 12 September 2020 | | 266 × 235 (28 KB) | Nilesj (talk | contribs) | recompiled to clarify this is in the public domain; also slightly adjusted two arrows |
| 20:14, 14 February 2019 |  | 268 × 238 (28 KB) | Omaranto (talk | contribs) | User created page with UploadWizard |
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