Praying Mantises are among the most recognised of insects. They have the reputation of being "good guys" because they eat other insects and that makes them beneficial. A world catalogue of mantises (or mantids, if you prefer) can be found on the Mantis Species File: http://mantodea.speciesfile.org/HomePage/Mantodea/HomePage.aspx
Australia has a substantial diversity of mantids. They occur in most habitats and have varied life styles. Here in the rainforest we have a number of species that you don't see elsewhere--out in the open woodlands, for example. But many of them seem to occur in both habitats.
In the first instance below, the family, subfamily and tribe are listed just to show the diversity in just the few species noted.
Kongobatha diademata Hebard; Iridopterygidae; Tropidomantinae; Tropidomantini is a fast-moving little mantis that lives in both the rainforest habitat but can also be found on shrubbery in open woodland habitats where it can be quite dry.
Kongobatha diademata Hebard
Taxonomists use a wide variety of characters in determining mantis species. This Garden Mantid provides an example.
Male Ciulfina rentzi, note the genitalia at the tip of the abdomen.
Taxonomists rely on features of the genitalia almost as a final assessment of the identity of a species. This works in most groups but not all. In fact, a professor of mine once said that all a taxonomist needs is a locality label and the male genitalia to identify a species. That is ridiculous, of course, but there is some truth in it.
Recently our colleague, Ms Sydney K Brannoch gained some notoriety, especially in feminist circles, when she described a mantis species based on a female and female internal characteristics. She named it in honour of one of her "heros" US Supreme Court Justice Ruth Bader Ginsburg. You can see her interview on the subject: https://www.cmnh.org/science-news/announcements/ilomantis-ginsburgae. The point of the study was to illustrate that there are important characters distinctive in females as well as males. This has been shown in other groups as well. Grasshoppers are a good example.
A few more examples of local mantises
Nymph Ciulfina rentzi,
Male Ciulfina rentzi,
Ciulfina rentzi Howell, Ginn, Herberstein; Liturgusidae; Liturgusinae; Liturgusini is a diurnal mantis that is usually called a "tree runner" because it is mostly found on tree trunks where it hunts small insects. However, after dark the mantises move off their trunks onto adjacent vegetation to seek new sites. We make this observation repeatedly.
The type locality of this species, the place from which it was described, is the Cairns Botanic Gardens, Cairns!