Where does “Phasmatoidea” come from?

Phasmatoidea (Translingual) comes from Translingual Phasma, from New Latin phasma, from Ancient Greek φάσμα, from Ancient Greek φάσις, from Ancient Greek φαίνω, from English -type, from Ancient Greek τύπος, from Ancient Greek τύπτω — to push, to hit.

Ancestry of “Phasmatoidea”, step by step

Step	Language	Word	Meaning
1	Translingual	Phasma	—
2	New Latin	phasma	An apparation, specter, phantom
3	Ancient Greek	φάσμα	Apparition, phantom; Appearance, phenomenon;...
4	Ancient Greek	φάσις	appearance; utterance, statement, expression
5	Ancient Greek	φαίνω	I cause to appear, bring to light; I show,...
6	English	-type	impressed form; stamp; print; typical form; Used...
7	Ancient Greek	τύπος	A blow, pressing; The results of a blow: mark,...
8	Ancient Greek	τύπτω	to beat, strike, smite; to beat, strike oneself
9	Proto-Indo-European	(s)tewp-	to push, to stick
10	Proto-Indo-European	(s)tew-	to push, to hit

Every word from Proto-Indo-European (s)tew- →