Let G6,3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_{6,3}$$\end{document} be a hyperbolic polygon-group with boundary the Menger curve. Granier (Groupes discrets en g & eacute;om & eacute;trie hyperbolique-aspects effectifs, Universit & eacute; de Fribourg, 2015) constructed a discrete, convex cocompact and faithful representation rho\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho $$\end{document} of G6,3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_{6,3}$$\end{document} into PU(2,1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textbf{PU}(2,1)$$\end{document}. We show the 3-orbifold at infinity of rho(G6,3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho (G_{6,3})$$\end{document} is a closed hyperbolic 3-orbifold, with underlying space the 3-sphere and singular locus the Z3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {Z}}_3$$\end{document}-coned chain-link C(6,-2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C(6,-2)$$\end{document}. This answers the second part of Kapovich's Conjecture 10.6 in Kapovich (in: In the tradition of thurston II. Geometry and groups, Springer, Cham, 2022), and it also provides the second explicit example of a closed hyperbolic 3-orbifold that admits a uniformizable spherical CR-structure after Schwartz's first example in Schwartz (Invent Math 151(2):221-295, 2003).
