Family: Unicells or cells loosely attached forming hyphae; cell body varied in shape, a constriction at the center in most species; cell walls consisting of two or more parts, with small pores and various ornaments (Illustrations of The Japanese Fresh-water Algae, 1977).
Genus: Cell body small, length = width, strong constriction at its center; semicells inverted triangular, ellipsoidal, rectangular, etc. in shape; straight or slightly curved spiny projections at each corner; one pyrenoid in each semicell; cell wall smooth (Illustrations of The Japanese Fresh-water Algae, 1977).

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Section: Tetracanthum: Lateral margins lack spiny projections -->> Genus: Staurodesmus Teiling 1948
Semicells elliptical in shape
A. subulatus var. subaequalis or A. rhomboides ? 38 x 27 μm USA, 1999	A. subulatus var. nordstedtii 31 x 31 μm Uruguay, 1999	A. convergens 4 samples 31-33 x 33-38 μm 2006-2008
Semicells inverted semicircle/hexagonal		Semicells inverted trapezoid
A. incus 18 samples 15-25 x 13-23 μm 199?-2008		A. controversus ? 18 x 15 μm Tenbo marsh Tsugaike highland Nagano, 2005
Semicells inverted quadrangular		Semicells inverted triangular
A. extensus 13 samples 15-26 x 13-27 μm 1999-2008		A. triangularis 6 samples var. latiusculum ? 17-22 μm 2004-2008	A. triangularis 6 samples var. acuminatum ? 17-22 μm 2004-2008
Section: Octacanthum: Spiny projections present at lateral margins -->> genus Octacanthium Compère 1996 or genus Xanthidium
A. octocornis 5 samples 21-31 x 17-26 μm 2005-2008

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