[1][2][3] The species was first described in 1993 by Jane Fromont as Amphimedon terpenensis from a specimen collected at a depth of 19 m on MacGillivray Reef, Lizard Island in the Great Barrier Reef.

[1][4] The species epithet, terpenensis, was given because of the large proportion of terpenes in this sponge.

[4] P. terpenensis is a red-brown sponge with a thin maroon band due partially to the sponge's pigment but also to a symbiont cyanobacteria.

[4] It is tall and sometimes the branches look like flattened organ pipes.

[4] It grows on reefs in full light, on dead coral or rock at depths of 10 to 20.