I've got a Greek-only font (no Latin characters) that polyglossia none the less refuses to recognize as a Greek font!

Minimum example:
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Code, edit and compile here:
\documentclass[a5paper, openany, 10pt]{book}\usepackage{fontspec}\defaultfontfeatures{Mapping=tex-text}\setmainfont{GFS Didot Classic}\usepackage{polyglossia}\setmainlanguage[variant=poly]{greek}\begin{document}Ἤμουν στὸ σπίτι μου ἐγὼ.\end{document}
The error message I get is the following:
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! Package polyglossia Error: The current roman font does not contain the Greek script!(polyglossia) Please define \greekfont with \newfontfamily.See the polyglossia package documentation for explanation.Type H <return> for immediate help.