Geastrum sp. (Geastrum sp.)

The species of Geastrum are known colloquially as earthstars. Each mature fruitbody consists of a puffball-like spore sac atop a star-like base. Some species are easy to identify visually, others are not. Before you started looking at microscopic details, some of the questions you'd ask when trying to identify a Geastrum are:   

 Does the spore sac sit directly on the base or is it held up by a stem (and if so, what is its size)?

 Are the arms of the base hygroscopic (in other words, do they fold inwards in dry conditions and open out in moist conditions)?

 Does soil/debris adhere tightly to the undersides of the basal arms or are they free of soil/debris (or at least where any soil/debris is easily removed by light brushing)?    

 What is the nature of the apical mouth, through which the spores puff out? Two examples are a (1) conical, strongly pleated mouth (as shown here, http://www.cpbr.gov.au/fungi/images-captions/geastrum-sp-ostiole-0144.html) and (2) a fibrillose mouth (http://www.cpbr.gov.au/fungi/images-captions/geastrum-sp-ostiole-0143.html).  

 You'd also note colour, texture and size.