j) Aquatic floating herbs with long petioles sheathing at the base; 3 upper stamens included, 3 lower ones more or less exserted. =Pontederiaceæ= jj) Not aquatic or rarely subaquatic; stamens 6, more or less equal; =Liliaceæ= hh) Perianth absent or very rudimentary; carpel 1; submerged aquatics with branched filiform smooth or muricate stems, flowers diœcious or monœcious, axillary, small. =Naiadaceæ= ff) Flowers unisexual, collected into involucrate heads or dense spikes: g) Flowers in dense involucrate heads; low herbs often stemless with mostly densely crowded leaves. =Eriocaulaceæ= gg) Flowers in spadices; trees or shrubs, the stems bearing thick aerial roots. =Pandanaceæ= ggg) Flowers in dense cylindric spikes; aquatic herbs with linear alternate leaves and creeping rhizomes. =Typhaceæ= dd) Ovary inferior: e) Stamens 3-6: f) Ovules parietal: g) Leaves not divided; stigma not umbrella-shaped, flowers hermaphrodite or unisexual. =Hydrocharitaceæ= gg) Leaves divided; stigma umbrella-shaped; leaves large, divided. =Taccaceæ= ff) Ovules axile, basal or apical: g) Perianth-lobes or segments 3-6: h) Stamens 6 or 3; flowers very small, diœcious; stems climbing. =Dioscoreaceæ= hh) Stamens 6; flowers conspicuous, hermaphrodite; stems not climbing. =Amaryllidaceæ= hhh) Stamens 3; inserted opposite the outer perianth-segments; not climbing. =Iridaceæ= gg) Perianth-segment 1; stamens 5, rarely 6; leaves with pinnate nervation; tall plants. =Musaceæ= ee) Stamen 1: f) Flowers actinomorphic or nearly so: g) Anthers 2-celled; ovules numerous; perianth-segments united below. =Zingiberaceæ= gg) Anthers 1-celled; ovules solitary in each cell; petiole thickened towards the apex. =Marantaceæ=