File:Associahedron K5 front.svg

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Summary

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_front.png; updated here for svg
Author Nilesj


Tikz Source

\begin{tikzpicture}[x=1.18mm,y=1mm,scale=1.6]
    % node numbering is from Tamari's thesis
    % parenthesization is reversed
    \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) {((a(bc))d)e}
    (7.3,-1.6) node (1210) {(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) {\cdot}
    (0,-5) node (2101) {\cdot}
    (-5.5,5) node (3001) {\cdot}
    (5.5,5) node (3100) {\cdot}
    ;
    \path[->,dashed, color=black!50!white]
    (2011) edge (3001)
    (2200) edge (3100)
    (1201) edge (2101)
    (3010) edge (4000)
    %
    (2101) edge (3001)
    (3001) edge (4000)
    (2101) edge (3100)
    (3100) edge (4000)
    ;
    \path[->] %arrows
    (1120) edge (1210)
    (1210) edge (2110)
    (2110) edge (3010)
    (1120) edge (2020)
    (2020) edge (3010)
    %
    (1210) edge (1300)
    (1111) edge (1120)
    (1111) edge (1201)
    (1201) edge (1300)
    %
    (1111) edge (2011)
    (2011) edge (2020)
    %
    (1300) edge (2200)
    (2110) edge (2200)
    ;
\end{tikzpicture}

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero 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.

Captions

The 3-dimensional associahedron

Items portrayed in this file

depicts

14 February 2019

image/svg+xml

3ac05e84d843e191e6db59163f588881a8bf8de9

27,164 byte

235 pixel

266 pixel

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current22:29, 12 September 2020Thumbnail for version as of 22:29, 12 September 2020266 × 235 (27 KB)Nilesjrecompiled to clarify this is in the public domain
20:14, 14 February 2019Thumbnail for version as of 20:14, 14 February 2019268 × 238 (27 KB)OmarantoUser created page with UploadWizard
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