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Homalozoa is an obsolete extinct subphylum of Paleozoic Era echinoderms, prehistoric marine invertebrates. They are also referred to as carpoids.

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Cincta is an extinct class of echinoderms that lived only in the Middle Cambrian epoch. Homostelea is a junior synonym. The classification of cinctans is controversial, but they are probably part of the echinoderm stem group.

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Cornuta is an extinct order of echinoderms. Along with the mitrates, they form one half of the Stylophora.

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Cothurnocystidae is an extinct family of stylophoran echinoderms in the order Cornuta.

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Cothurnocystis is a genus of small enigmatic echinoderms that lived during the Ordovician. Individual animals had a flat boot-shaped body and a thin rod-shaped appendage that may be a stem, or analogous to a foot or a tail. Fossils of Cothurnocystis species have been found in Nevada, Scotland, Czech Republic, France and Morocco.

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Ctenocystoidea is an extinct clade of echinoderms, which lived during the Cambrian and Ordovician periods. Unlike other echinoderms, ctenocystoids had bilateral symmetry, or were only very slightly asymmetrical. They are believed to be one of the earliest-diverging branches of echinoderms, with their bilateral symmetry a trait shared with other deuterostomes. Ctenocystoids were once classified in the taxon Homalozoa, also known as Carpoidea, alongside cinctans, solutes, and stylophorans. Homalozoa is now recognized as a polyphyletic group of echinoderms without radial symmetry. Ctenocystoids were geographically widespread during the Middle Cambrian, with one species surviving into the Late Ordovician.

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Cincta is an extinct class of echinoderms that lived only in the Middle Cambrian epoch. Homostelea is a junior synonym. The classification of cinctans is controversial, but they are probably part of the echinoderm stem group.

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The stylophorans are an extinct, possibly polyphyletic group allied to the Paleozoic Era echinoderms, comprising the prehistoric cornutes and mitrates. It is synonymous with the subphylum Calcichordata. Their unusual appearances have led to a variety of very different reconstructions of their anatomy, how they lived, and their relationships to other organisms.