This fungus was once placed in Geastrum. In dry weather the arms fold back over the spore sac. In the northern hemisphere this species forms symbiotic associations with various trees. Do you know if there are any exotic trees nearby (e.g. elm, oak, pine, birch)?
Thanks Heino1, the garden nearby them is planted out with exotics, including with a few topiary conifers (Cupressus I think) but none of the trees you mention. Within ~50m the trees in the street are mainly tea trees, Photinia and eucalypts. If it might be relevant, the mulch and wood debris in which the fungus was found looks as though it may have been brought in from elsewhere.