Family: Colonies of a fixed number of cells (4, 8, 16, 32, or more) arranged 2- or 3-dimensionally; cells spherical, ellipsoidal, polygonal, etc. in shape; chloroplasts 1 or several, plate-like in shape, with 1 pyrenoid; asexual reproduction by autocoenobium (Illustrations of The Japanese Fresh-water Algae, 1977).
Genus: Arrangement of 4 daughter cells flat and rectangular in shape, forming composite coenobium; without gelatinous sheaths, no hairly projections (Illustrations of the Japanese Freshwater Algae, 1977).

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Cell body ellipsoidal - ovoidal - spherical in shape
C. rectangularis 11 x 6 μm 7 x 4 μm Tsukuba Ibaraki, 2002	C. lauterbornii 9.5 x 8 μm Japan, 2000	C. quadrata 6 x 3.5 μm Toneri Park Tokyo, 2001	C. quadrata ? 6 x 3.5-5 μm Maruyama Park Ageo Saitama, 2002
C. quadrata ? 5-6 x 4-5 μm Watarase river Ashikaga Tochigi, 2004	C. quadrata 4.5-6 x 4-5 μm near Yamaguchi Univ. Yamaguchi, 2004	C. quadrata ? μm Kareki-numa Nikko Tochigi, 2008
Cell body slightly curved
C. crucifera: 13 samples
C. crucifera 9.5 x 4.7 μm Ueno Tokyo, 2001	C. crucifera 6 x 4 μm Bessho numa Saitama, 2001	C. crucifera 7 x 4.5 μm Mizumoto park Tokyo, 2001	C. crucifera 7 x 4.5 μm Abiko Chiba, 2000
Cell body triangular in shape
C. tetrapedia: 6 samples
C. tetrapedia cell 5.5 x 2.3 μm colony 16 μm Ueno Tokyo, 2001	C. tetrapedia 3 x 4 μm colony 12 μm Nishi-Urawa Saitama, 2001	C. tetrapedia 5 x 6 μm Mizumoto park Tokyo, 2001	C. tetrapedia μm Higusa-numa Hikari Chiba, 2003
C. fenestrata ? or Tetrastrum ? 4.5 x 3 μm Ueno Tokyo, 2001	C. fenestrata 15 x 13 μm Omine-numa 6 Minakami Gunma, 2007	C. fenestrata μm Karayama-ike Iiyama Nagano, 2008

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