Polymastia Bowerbank, 1864: 177.
Penicillaria Gray, 1867: 527.
Rinalda Schmidt, 1870: 51.
TYPE SPECIES. — Spongia mamillaris Müller, 1806: 44 (by monotypy).
DIAGNOSIS (from Boury-Esnault 2002). — Polymastiidae, thickly encrusting, spherical or cushionshaped, always with papillae. Choanosomal skeleton composed of radial tracts of principal spicules between which free spicules are scattered. Ectosomal skeleton composed of at least two layers, the superficial one is a palisade of small tylostyles, the lower layer is made of intermediary spicules, tangential to the surface. The principal spicules can be tylostyles, subtylostyles, styles or strongyloxeas, intermediary spicules are most often tylostyles, and ectosomal spicules are always tylostyles.