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In this note we establish the existence of all Curtis-Tits groups and Phangroups with $3$-spherical diagram as classified previously and investigate someof their geometric and group theoretic properties. Whereas it is known thatorientable Curtis-Tits groups with spherical or non-spherical and non-affinediagram are almost simple, we show that non-orientable Curtis-Tits groups areacylindrically hyperbolic and therefore have infinitely many infinite-indexnormal subgroups. However, we also provide concrete examples of non-orientableCurtis-Tits groups whose quotients are finite simple groups of Lie type.

Realizations and properties of $3$-spherical Curtis-Tits Groups and Phan groups