Abstract
Related to a Coxeter group are certain sets of tangents of the deltoid with evenly distributed orientations forming simplicial line configurations. These configurations are used to construct curves and surfaces with [Formula: see text] singularities. Other surfaces associated with invariants of exceptional complex reflection groups are considered. A new lower bound for the maximal number of [Formula: see text] singularities in a sextic surface is obtained. Several Calabi–Yau threefolds defined as double coverings of the complex projective 3-space branched along nodal octic surfaces and Calabi–Yau quintic threefolds are analyzed. The Hodge numbers of a small resolution of all the nodes of the singular threefolds are obtained.
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