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. 2018 Sep 25;2(3):177–231. doi: 10.1007/s41468-018-0021-5

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© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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Fig. 3 — Let $g \in G F_{1}$ with $g = \bar{x_{1} x_{2} x_{3} x_{4}}$ , where $d_{0} (x_{1}) = d_{0} {(x_{2})}^{- 1}$ , $d_{0} (x_{3}) = d_{0} {(x_{4})}^{- 1}$ , $d_{2} (x_{1}) = d_{1} (x_{2})$ , $d_{2} (x_{2}) = d_{1} (x_{1})$ , $d_{1} (x_{3}) = d_{2} (x_{3})$ and $d_{1} (x_{4}) = d_{2} (x_{4})$ . Simplicial set Y is then obtained by identifying faces of triangles $y_{1}, y_{2}, y_{3}, y_{4}$ as pictured here. One can see $| Y | = S^{2} \lor S^{2}$